Protestors in Ukraine have vowed to carry on fighting after rejecting a government offer.
Firebombs have been hurled, with police fighting back with tear gas, as violent clashes continued in the capital, Kiev.
Britain welcomed the offer by embattled president Viktor Yanukovych to offer the country's second-highest job to opposition leader Arseniy Yatsenyuk.
STORY CONTINUES BELOW:
Ukraine Unrest
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Medics transport an injured protester during an attack of the Ukrainian House building in central Kiev, Ukraine, early Sunday, Jan. 26, 2014. New violence erupted in Ukraine's capital during the night as a large crowd attacked the government exposition and conference hall where police were stationed inside. Early Sunday, demonstrators were throwing firebombs into the Ukrainian House building and setting off fireworks, and police responded with tear gas. (AP Photo/Evgeny Feldman) (credit:AP)
Protests Continue In Kiev As The Opposition Calls For A Snap Election(02 of41)
KIEV, UKRAINE - JANUARY 26: Fireworks fired by anti-government protesters explode inside the Ukrainian House, which the protesters attempted to take over, on January 26, 2014 in Kiev, Ukraine. After two months of primarily peaceful anti-government protests in the city center, new laws meant to end the protest movement have sparked violent clashes in recent days. (Photo by Brendan Hoffman/Getty Images) (credit:Getty Images)
Protests Continue In Kiev As The Opposition Calls For A Snap Election(03 of41)
KIEV, UKRAINE - JANUARY 26: An anti-government protester talks with police through a broken window in the Ukrainian House on January 26, 2014 in Kiev, Ukraine. After two months of primarily peaceful anti-government protests in the city center, new laws meant to end the protest movement have sparked violent clashes in recent days. (Photo by Brendan Hoffman/Getty Images) (credit:Getty Images)
Protests Continue In Kiev As The Opposition Calls For A Snap Election(04 of41)
KIEV, UKRAINE - JANUARY 25: Anti-government protesters walk among burned buses on Hrushevskoho Street near Dynamo stadium on January 25, 2014 in Kiev, Ukraine. After two months of primarily peaceful anti-government protests in the city center, new laws meant to end the protest movement have sparked violent clashes in recent days. (Photo by Brendan Hoffman/Getty Images) (credit:Getty Images)
Protests Continue In Kiev As The Opposition Calls For A Snap Election(05 of41)
KIEV, UKRAINE - JANUARY 26: Police hold their shields for protection inside the Ukrainian House, which anti-government protesters attempted to take over, on January 26, 2014 in Kiev, Ukraine. After two months of primarily peaceful anti-government protests in the city center, new laws meant to end the protest movement have sparked violent clashes in recent days. (Photo by Brendan Hoffman/Getty Images) (credit:Getty Images)
Protests Continue In Kiev As The Opposition Calls For A Snap Election(06 of41)
KIEV, UKRAINE - JANUARY 26: Anti-government protesters stand outside the Ukrainian House, which they attempted to take over, on January 26, 2014 in Kiev, Ukraine. After two months of primarily peaceful anti-government protests in the city center, new laws meant to end the protest movement have sparked violent clashes in recent days. (Photo by Brendan Hoffman/Getty Images) (credit:Getty Images)
UKRAINE-UNREST-EU-RUSSIA-POLITICS(07 of41)
Opposition activists storm the Ukrainian House, where the riot police have based their troops, in Kiev on January 26, 2014. The Ukrainian opposition vowed to press on with protests despite an offer of top posts made by President Viktor Yanukovych as protesters took control of another building in the capital Sunday. Ukrainian television said that around 200 police forces left the Ukrainian House in central Kiev, a Soviet-era exhibition hall used by troops as a base, by a side entrance. AFP PHOTO / SERGEI SUPINSKY (Photo credit should read SERGEI SUPINSKY/AFP/Getty Images) (credit:Getty Images)
UKRAINE-UNREST-EU-RUSSIA-POLITICS(08 of41)
Opposition activists storm the Ukrainian House, where the riot police have based their troops, in Kiev on January 26, 2014. The Ukrainian opposition vowed to press on with protests despite an offer of top posts made by President Viktor Yanukovych as protesters took control of another building in the capital Sunday. Ukrainian television said that around 200 police forces left the Ukrainian House in central Kiev, a Soviet-era exhibition hall used by troops as a base, by a side entrance. AFP PHOTO / SERGEI SUPINSKY (Photo credit should read SERGEI SUPINSKY/AFP/Getty Images) (credit:Getty Images)
UKRAINE-UNREST-EU-RUSSIA-POLITICS(09 of41)
Opposition activists storm the Ukrainian House, where the riot police have based their troops, in Kiev on January 26, 2014. The Ukrainian opposition vowed to press on with protests despite an offer of top posts made by President Viktor Yanukovych as protesters took control of another building in the capital Sunday. Ukrainian television said that around 200 police forces left the Ukrainian House in central Kiev, a Soviet-era exhibition hall used by troops as a base, by a side entrance. AFP PHOTO / SERGEI SUPINSKY (Photo credit should read SERGEI SUPINSKY/AFP/Getty Images) (credit:Getty Images)
UKRAINE-UNREST-EU-RUSSIA-POLITICS(10 of41)
Opposition activists storm the Ukrainian House, where the riot police have based their troops, in Kiev on January 26, 2014. The Ukrainian opposition vowed to press on with protests despite an offer of top posts made by President Viktor Yanukovych as protesters took control of another building in the capital Sunday. Ukrainian television said that around 200 police forces left the Ukrainian House in central Kiev, a Soviet-era exhibition hall used by troops as a base, by a side entrance. AFP PHOTO / SERGEI SUPINSKY (Photo credit should read SERGEI SUPINSKY/AFP/Getty Images) (credit:Getty Images)
Protests Continue In Kiev As The Opposition Calls For A Snap Election(11 of41)
KIEV, UKRAINE - JANUARY 25: An anti-government protester kicks in a window of the Ukrainian House, which protesters attempted to take over, on January 25, 2014 in Kiev, Ukraine. After two months of primarily peaceful anti-government protests in the city center, new laws meant to end the protest movement have sparked violent clashes in recent days. (Photo by Brendan Hoffman/Getty Images) (credit:Getty Images)
Protests Continue In Kiev As The Opposition Calls For A Snap Election(12 of41)
KIEV, UKRAINE - JANUARY 26: Anti-government protesters stand outside the Ukrainian House, which they attempted to take over, on January 26, 2014 in Kiev, Ukraine. After two months of primarily peaceful anti-government protests in the city center, new laws meant to end the protest movement have sparked violent clashes in recent days. (Photo by Brendan Hoffman/Getty Images) (credit:Getty Images)
UKRAINE-EU-RUSSIA-UNREST-POLITICS(13 of41)
Anti-government protesters burn tires at the flashpoint Grushevsky Street in the central Kiev late January 25, 2014. Ukrainian President Viktor Yanukovych on Saturday offered sweeping concessions for the opposition, including the prime minister's post, to end a deadly crisis but his opponents vowed to press on with protests until all their demands are met. Tensions continued to boil in the streets of Kiev, with stick-wielding protesters in helmets seen throwing Molotov cocktails and smashing in the windows of a Soviet-era building in Kiev used as a temporary base by the security forces. AFP PHOTO / ARIS MESSINIS (Photo credit should read ARIS MESSINIS/AFP/Getty Images) (credit:Getty Images)
UKRAINE-EU-RUSSIA-UNREST-POLITICS(14 of41)
Anti-government protesters gather around the fire to get warm at the flashpoint Grushevsky Street in central Kiev late January 25, 2014. Ukrainian President Viktor Yanukovych on Saturday offered sweeping concessions for the opposition, including the prime minister's post, to end a deadly crisis but his opponents vowed to press on with protests until all their demands are met. Tensions continued to boil in the streets of Kiev, with stick-wielding protesters in helmets seen throwing Molotov cocktails and smashing in the windows of a Soviet-era building in Kiev used as a temporary base by the security forces. AFP PHOTO / ARIS MESSINIS (Photo credit should read ARIS MESSINIS/AFP/Getty Images) (credit:Getty Images)
UKRAINE-EU-RUSSIA-UNREST-POLITICS(15 of41)
An anti-government protesters gather behind a road block at the flashpoint Grushevsky Street in the central Kiev late January 25, 2014. Ukrainian President Viktor Yanukovych on Saturday offered sweeping concessions for the opposition, including the prime minister's post, to end a deadly crisis but his opponents vowed to press on with protests until all their demands are met. Tensions continued to boil in the streets of Kiev, with stick-wielding protesters in helmets seen throwing Molotov cocktails and smashing in the windows of a Soviet-era building in Kiev used as a temporary base by the security forces. AFP PHOTO / ARIS MESSINIS (Photo credit should read ARIS MESSINIS/AFP/Getty Images) (credit:Getty Images)
UKRAINE-EU-RUSSIA-UNREST-POLITICS(16 of41)
Anti-government protesters stand at a road block in Kiev on January 26, 2014. The Ukrainian opposition vowed to press on with protests despite an offer of top posts made by President Viktor Yanukovych as protesters took control of another building in the capital Sunday. Two months after the protests began in November over his decision to back out of an EU pact Yanukovych on Saturday offered to share leadership with Arseniy Yatsenyuk as prime minister and Vitali Klitschko as deputy prime minister in a bid to end the crisis.AFP PHOTO / ARIS MESSINIS (Photo credit should read ARIS MESSINIS/AFP/Getty Images) (credit:Getty Images)
UKRAINE-EU-RUSSIA-UNREST-POLITICS(17 of41)
An anti-government protester stands in front of a fire to get warm at the flashpoint Grushevsky Street in the central Kiev late January 25, 2014. Ukrainian President Viktor Yanukovych on Saturday offered sweeping concessions for the opposition, including the prime minister's post, to end a deadly crisis but his opponents vowed to press on with protests until all their demands are met. Tensions continued to boil in the streets of Kiev, with stick-wielding protesters in helmets seen throwing Molotov cocktails and smashing in the windows of a Soviet-era building in Kiev used as a temporary base by the security forces. AFP PHOTO / ARIS MESSINIS (Photo credit should read ARIS MESSINIS/AFP/Getty Images) (credit:Getty Images)
Protests Continue In Kiev As The Opposition Calls For A Snap Election(18 of41)
KIEV, UKRAINE - JANUARY 26: Anti-government protesters attempt to take over the Ukrainian House on January 26, 2014 in Kiev, Ukraine. After two months of primarily peaceful anti-government protests in the city center, new laws meant to end the protest movement have sparked violent clashes in recent days. (Photo by Brendan Hoffman/Getty Images) (credit:Getty Images)
UKRAINE-EU-RUSSIA-UNREST-POLITICS(19 of41)
Anti-government protesters gather at the flashpoint Grushevsky Street in the central Kiev late January 25, 2014. Ukrainian President Viktor Yanukovych on Saturday offered sweeping concessions for the opposition, including the prime minister's post, to end a deadly crisis but his opponents vowed to press on with protests until all their demands are met. Tensions continued to boil in the streets of Kiev, with stick-wielding protesters in helmets seen throwing Molotov cocktails and smashing in the windows of a Soviet-era building in Kiev used as a temporary base by the security forces. AFP PHOTO / ARIS MESSINIS (Photo credit should read ARIS MESSINIS/AFP/Getty Images) (credit:Getty Images)
Protests Continue In Kiev As The Opposition Calls For A Snap Election(20 of41)
KIEV, UKRAINE - JANUARY 26: Anti-government protesters stand outside the Ukrainian House, which they attempted to take over, on January 26, 2014 in Kiev, Ukraine. After two months of primarily peaceful anti-government protests in the city center, new laws meant to end the protest movement have sparked violent clashes in recent days. (Photo by Brendan Hoffman/Getty Images) (credit:Getty Images)
UKRAINE-EU-RUSSIA-UNREST-POLITICS(21 of41)
An injured anti-government protester reacts in the central Kiev late January 25, 2014. Ukrainian President Viktor Yanukovych on Saturday offered sweeping concessions for the opposition, including the prime minister's post, to end a deadly crisis but his opponents vowed to press on with protests until all their demands are met. Tensions continued to boil in the streets of Kiev, with stick-wielding protesters in helmets seen throwing Molotov cocktails and smashing in the windows of a Soviet-era building in Kiev used as a temporary base by the security forces. AFP PHOTO / ARIS MESSINIS (Photo credit should read ARIS MESSINIS/AFP/Getty Images) (credit:Getty Images)
Protests Continue In Kiev As The Opposition Calls For A Snap Election(22 of41)
KIEV, UKRAINE - JANUARY 26: Anti-government protesters stand outside the Ukrainian House, which they attempted to take over, on January 26, 2014 in Kiev, Ukraine. After two months of primarily peaceful anti-government protests in the city center, new laws meant to end the protest movement have sparked violent clashes in recent days. (Photo by Brendan Hoffman/Getty Images) (credit:Getty Images)
UKRAINE-UNREST-EU-RUSSIA-POLITICS(23 of41)
Opposition activists storm the Ukrainian House, where the riot police have based their troops, in Kiev on January 26, 2014. The Ukrainian opposition vowed to press on with protests despite an offer of top posts made by President Viktor Yanukovych as protesters took control of another building in the capital Sunday. Ukrainian television said that around 200 police forces left the Ukrainian House in central Kiev, a Soviet-era exhibition hall used by troops as a base, by a side entrance. AFP PHOTO / SERGEI SUPINSKY (Photo credit should read SERGEI SUPINSKY/AFP/Getty Images) (credit:Getty Images)
UKRAINE-EU-RUSSIA-UNREST-POLITICS(24 of41)
Anti-government protesters stand at a road block in Kiev on January 26, 2014. The Ukrainian opposition vowed to press on with protests despite an offer of top posts made by President Viktor Yanukovych as protesters took control of another building in the capital Sunday. Two months after the protests began in November over his decision to back out of an EU pact Yanukovych on Saturday offered to share leadership with Arseniy Yatsenyuk as prime minister and Vitali Klitschko as deputy prime minister in a bid to end the crisis.AFP PHOTO / ARIS MESSINIS (Photo credit should read ARIS MESSINIS/AFP/Getty Images) (credit:Getty Images)
UKRAINE-EU-RUSSIA-UNREST-POLITICS(25 of41)
An anti-government protester looks on as he rests at a road block in Kiev on January 26, 2014. The Ukrainian opposition vowed to press on with protests despite an offer of top posts made by President Viktor Yanukovych as protesters took control of another building in the capital Sunday. Two months after the protests began in November over his decision to back out of an EU pact Yanukovych on Saturday offered to share leadership with Arseniy Yatsenyuk as prime minister and Vitali Klitschko as deputy prime minister in a bid to end the crisis.AFP PHOTO / ARIS MESSINIS (Photo credit should read ARIS MESSINIS/AFP/Getty Images) (credit:Getty Images)
UKRAINE-EU-RUSSIA-UNREST-POLITICS(26 of41)
Anti-government protesters stand at a road block in Kiev on January 26, 2014. The Ukrainian opposition vowed to press on with protests despite an offer of top posts made by President Viktor Yanukovych as protesters took control of another building in the capital Sunday. Two months after the protests began in November over his decision to back out of an EU pact Yanukovych on Saturday offered to share leadership with Arseniy Yatsenyuk as prime minister and Vitali Klitschko as deputy prime minister in a bid to end the crisis.AFP PHOTO / ARIS MESSINIS (Photo credit should read ARIS MESSINIS/AFP/Getty Images) (credit:Getty Images)
UKRAINE-EU-RUSSIA-UNREST-POLITICS(27 of41)
An anti-government protester looks on as he rests at a road block in Kiev on January 26, 2014. The Ukrainian opposition vowed to press on with protests despite an offer of top posts made by President Viktor Yanukovych as protesters took control of another building in the capital Sunday. Two months after the protests began in November over his decision to back out of an EU pact Yanukovych on Saturday offered to share leadership with Arseniy Yatsenyuk as prime minister and Vitali Klitschko as deputy prime minister in a bid to end the crisis.AFP PHOTO / ARIS MESSINIS (Photo credit should read ARIS MESSINIS/AFP/Getty Images) (credit:Getty Images)
UKRAINE-EU-RUSSIA-UNREST-POLITICS(28 of41)
An anti-government protester rests at a road block in Kiev on January 26, 2014. The Ukrainian opposition vowed to press on with protests despite an offer of top posts made by President Viktor Yanukovych as protesters took control of another building in the capital Sunday. Two months after the protests began in November over his decision to back out of an EU pact Yanukovych on Saturday offered to share leadership with Arseniy Yatsenyuk as prime minister and Vitali Klitschko as deputy prime minister in a bid to end the crisis.AFP PHOTO / ARIS MESSINIS (Photo credit should read ARIS MESSINIS/AFP/Getty Images) (credit:Getty Images)
UKRAINE-EU-RUSSIA-UNREST-POLITICS(29 of41)
Anti-government protesters rest at a road block in Kiev on January 26, 2014. The Ukrainian opposition vowed to press on with protests despite an offer of top posts made by President Viktor Yanukovych as protesters took control of another building in the capital Sunday. Two months after the protests began in November over his decision to back out of an EU pact Yanukovych on Saturday offered to share leadership with Arseniy Yatsenyuk as prime minister and Vitali Klitschko as deputy prime minister in a bid to end the crisis.AFP PHOTO / ARIS MESSINIS (Photo credit should read ARIS MESSINIS/AFP/Getty Images) (credit:Getty Images)
UKRAINE-EU-RUSSIA-UNREST-POLITICS(30 of41)
Anti-government protesters stand at a road block in Kiev on January 26, 2014. The Ukrainian opposition vowed to press on with protests despite an offer of top posts made by President Viktor Yanukovych as protesters took control of another building in the capital Sunday. Two months after the protests began in November over his decision to back out of an EU pact Yanukovych on Saturday offered to share leadership with Arseniy Yatsenyuk as prime minister and Vitali Klitschko as deputy prime minister in a bid to end the crisis.AFP PHOTO / ARIS MESSINIS (Photo credit should read ARIS MESSINIS/AFP/Getty Images) (credit:Getty Images)
UKRAINE-UNREST-EU-RUSSIA-POLITICS(31 of41)
Opposition activists storm the Ukrainian House, where the riot police have based their troops, in Kiev on January 26, 2014. The Ukrainian opposition vowed to press on with protests despite an offer of top posts made by President Viktor Yanukovych as protesters took control of another building in the capital Sunday. Ukrainian television said that around 200 police forces left the Ukrainian House in central Kiev, a Soviet-era exhibition hall used by troops as a base, by a side entrance. AFP PHOTO / SERGEI SUPINSKY (Photo credit should read SERGEI SUPINSKY/AFP/Getty Images) (credit:Getty Images)
UKRAINE-EU-RUSSIA-UNREST-POLITICS(32 of41)
Anti-government protesters rest at a road block in Kiev on January 26, 2014. The Ukrainian opposition vowed to press on with protests despite an offer of top posts made by President Viktor Yanukovych as protesters took control of another building in the capital Sunday. Two months after the protests began in November over his decision to back out of an EU pact Yanukovych on Saturday offered to share leadership with Arseniy Yatsenyuk as prime minister and Vitali Klitschko as deputy prime minister in a bid to end the crisis.AFP PHOTO / ARIS MESSINIS (Photo credit should read ARIS MESSINIS/AFP/Getty Images) (credit:Getty Images)
UKRAINE-EU-RUSSIA-UNREST-POLITICS(33 of41)
Anti-government protesters stand at a road block in Kiev on January 26, 2014. The Ukrainian opposition vowed to press on with protests despite an offer of top posts made by President Viktor Yanukovych as protesters took control of another building in the capital Sunday. Two months after the protests began in November over his decision to back out of an EU pact Yanukovych on Saturday offered to share leadership with Arseniy Yatsenyuk as prime minister and Vitali Klitschko as deputy prime minister in a bid to end the crisis.AFP PHOTO / ARIS MESSINIS (Photo credit should read ARIS MESSINIS/AFP/Getty Images) (credit:Getty Images)
UKRAINE-EU-RUSSIA-UNREST-POLITICS(34 of41)
Anti-government protesters stand at a road block in Kiev on January 26, 2014. The Ukrainian opposition vowed to press on with protests despite an offer of top posts made by President Viktor Yanukovych as protesters took control of another building in the capital Sunday. Two months after the protests began in November over his decision to back out of an EU pact Yanukovych on Saturday offered to share leadership with Arseniy Yatsenyuk as prime minister and Vitali Klitschko as deputy prime minister in a bid to end the crisis.AFP PHOTO / ARIS MESSINIS (Photo credit should read ARIS MESSINIS/AFP/Getty Images) (credit:Getty Images)
UKRAINE-EU-RUSSIA-UNREST-POLITICS(35 of41)
Anti-government protesters stand at a road block in Kiev on January 26, 2014. The Ukrainian opposition vowed to press on with protests despite an offer of top posts made by President Viktor Yanukovych as protesters took control of another building in the capital Sunday. Two months after the protests began in November over his decision to back out of an EU pact Yanukovych on Saturday offered to share leadership with Arseniy Yatsenyuk as prime minister and Vitali Klitschko as deputy prime minister in a bid to end the crisis.AFP PHOTO / ARIS MESSINIS (Photo credit should read ARIS MESSINIS/AFP/Getty Images) (credit:Getty Images)
UKRAINE-UNREST-EU-RUSSIA-POLITICS(36 of41)
A protester looks at police forces leaving the Ukrainian House, where they had based their troops, after opposition supporters stormed the flashpoint building and ousted them from the premises in new clashes in Kiev on January 26, 2014. The Ukrainian opposition vowed to press on with protests despite an offer of top posts made by President Viktor Yanukovych as protesters took control of another building in the capital Sunday. Ukrainian television said that around 200 police forces left the Ukrainian House in central Kiev, a Soviet-era exhibition hall used by troops as a base, by a side entrance. AFP PHOTO / SERGEI SUPINSKY (Photo credit should read SERGEI SUPINSKY/AFP/Getty Images) (credit:Getty Images)
UKRAINE-UNREST-EU-RUSSIA-POLITICS(37 of41)
Police forces leave the Ukrainian House, where they had based their troops, after opposition supporters stormed the flashpoint building and ousted them from the premises in new clashes in Kiev on January 26, 2014. The Ukrainian opposition vowed to press on with protests despite an offer of top posts made by President Viktor Yanukovych as protesters took control of another building in the capital Sunday. Ukrainian television said that around 200 police forces left the Ukrainian House in central Kiev, a Soviet-era exhibition hall used by troops as a base, by a side entrance. AFP PHOTO / SERGEI SUPINSKY (Photo credit should read SERGEI SUPINSKY/AFP/Getty Images) (credit:Getty Images)
UKRAINE-UNREST-EU-RUSSIA-POLITICS(38 of41)
Opposition activists storm the Ukrainian House, where the riot police have based their troops, in Kiev on January 26, 2014. The Ukrainian opposition vowed to press on with protests despite an offer of top posts made by President Viktor Yanukovych as protesters took control of another building in the capital Sunday. Ukrainian television said that around 200 police forces left the Ukrainian House in central Kiev, a Soviet-era exhibition hall used by troops as a base, by a side entrance. AFP PHOTO / SERGEI SUPINSKY (Photo credit should read SERGEI SUPINSKY/AFP/Getty Images) (credit:Getty Images)
UKRAINE-UNREST-EU-RUSSIA-POLITICS(39 of41)
Opposition activists carry a wounded person as they stormed the Ukrainian House, where the riot police have based their troops, in Kiev on January 26, 2014. The Ukrainian opposition vowed to press on with protests despite an offer of top posts made by President Viktor Yanukovych as protesters took control of another building in the capital Sunday. Ukrainian television said that around 200 police forces left the Ukrainian House in central Kiev, a Soviet-era exhibition hall used by troops as a base, by a side entrance. AFP PHOTO / SERGEI SUPINSKY (Photo credit should read SERGEI SUPINSKY/AFP/Getty Images) (credit:Getty Images)
UKRAINE-UNREST-EU-RUSSIA-POLITICS(40 of41)
Opposition activists guard a barricade on Independence Square in Kiev on January 26, 2014. The Ukrainian opposition vowed to press on with protests despite an offer of top posts made by President Viktor Yanukovych as protesters took control of another building in the capital Sunday. AFP PHOTO / SERGEI SUPINSKY (Photo credit should read SERGEI SUPINSKY/AFP/Getty Images) (credit:Getty Images)
UKRAINE-UNREST-EU-RUSSIA-POLITICS(41 of41)
Opposition leader head of UDAR (Punch) party Vitali Klitschko looks on as opposition protesters storm of Ukrainian House, where the riot police have based their troops, in Kiev on January 26, 2014. The Ukrainian opposition vowed to press on with protests despite an offer of top posts made by President Viktor Yanukovych as protesters took control of another building in the capital Sunday. AFP PHOTO / SERGEI SUPINSKY (Photo credit should read SERGEI SUPINSKY/AFP/Getty Images) (credit:Getty Images)
The offer also included a deputy-premier post for Vitali Klitschko, another top opposition leader.
But Klitschko, a former world heavyweight boxing champion, reiterated the opposition's demand for elections.
And a tweet from Yatsenyuk confirmed the unrest would continue.
The protests began in Kiev after Mr Yanukovych shelved a long-awaited trade pact with the EU in favour of securing a bailout loan from Russia. They boiled over into violence a week ago over the new anti-protest laws.
On Sunday morning, British Foreign Secretary William Hague urged Ukraine's government to repeal repressive laws and show restraint.
Speaking on BBC 1's The Andrew Marr Show, Hague said: "It is a big offer and it's good that they're talking, that the president is talking to the opposition leaders.
"We can't decide and judge for them in detail what sort of consensus they should create in the Ukraine but we can encourage them to do so.
"We are in touch with the government, I spoke to the foreign minister of the Ukraine on Friday night to urge that restraint in the face of violence and that repressive laws about freedom of expression and civil society should be changed, should be repealed.
"So we will keep encouraging both sides to talk to each other and encourage the Ukrainian government in that sort of direction."
Asked if he was worried Ukraine is on the tipping point and heading to complete breakdown and serious violence, Mr Hague said: "We are very worried about that.
"We should avoid saying things as foreign states that might make things worse but of course we're very worried about the situation in Ukraine and I don't think it need be seen as an East-West struggle.
"The fact is if Ukraine entered into the agreements with the EU that we've put forward - have free trade with the European Union - that would benefit the people of Ukraine. It would also benefit the people of Russia.
"It would benefit that entire region so we have to change the narrative about this."