Foreign Secretary William Hague pressed Russia to support international pressure on the Syrian regime after an escalation in violence in the crisis-hit country saw dozens of children massacred.
At a press conference on Monday Russia's foreign minister Sergei Lavrov agreed to support the peace plan put forward by UN-Arab League envoy Kofi Annan, who is in Damascus in a bid to re-instate the ceasefire, but said both sides were responsible for the violence.
Hague had gone into the meeting hoping to gain Russia's support for strong condemnation of the Syrian government and the removal of Assad.
Before arriving he tweeted: "In Moscow tomorrow. Will call on Russia to support rapid & unequivocal pressure on Assad regime and accountability for crimes.”
And after the talks, described as "honest and frank", the Foreign Secretary again called on Assad to quit.
During a joint press conference he said: "We have said all the way back from last August that finding a solution to this involves him standing aside."
But Mr Lavrov, sitting next to Mr Hague, said regime change in Damascus was "not the most important thing".
He told reporters: "For us it's not the most important thing who is in power in Syria.
"For us the main thing is to provide for the end of all violence."
The Syrian government was accused by the United Nations of an "outrageous use of force" against civilians in an attack on Friday that left more than 100 dead, including at least 49 children.
Another 41 people, including five women and eight children, have been killed by Syrian army shelling in the city of Hama in the past 24 hours, according to news agency Reuters.
Using information from an opposition group, it reported that tanks and soldiers opened fire on civilian neighbourhoods yesterday, in retaliation for rebel attacks on government road blocks.
Russia and China have so far been the principal opponents of stronger action against the Syrian regime by the UN.
China condemned the killings on Monday in Houla but stopped short of blaming the massacre of 100 people, including 49 children, at the door of President Bashar al-Assad's regime.
“The Chinese foreign ministry condemns in the strongest possible terms the cruel killings of ordinary citizens, especially women and children," the government said in a statement.
Russia has repeatedly warned that the international community risks sparking a civil war if it sides too heavily with opposition forces in Syria.
Mr Hague stressed that no one wanted this, but that the possibility now loomed even larger.
He said: "It isn't in the interests of Russia, it's not in anyone's interests, for Syria to descend into an even bloodier situation and into a full-scale civil war and that's now the danger.”
President Bashar Assad's regime was the focus of mounting uproar and condemnation for the Houla massacre, despite having denied being behind the slaughter.
Its claim that the bloodshed was caused by anti-government forces was dismissed by the international community, including Foreign Secretary William Hague.
After an emergency meeting last night, the UN Security Council said the Syrian government was responsible for artillery and tank shelling of residential areas.
It also condemned "the killing of civilians by shooting at close range and by severe physical abuse", adding that the "outrageous use of force" violated international law.
At least 108 people, including 49 children and 34 women, died in Friday's attacks, according to UN monitors.
Mr Hague said earlier that he was "absolutely sickened" by the massacre.
The Syrian charge d'affaires is to be summoned to the Foreign Office today to hear the Government's condemnation.
"It is a familiar tactic of the Assad regime to blame others for what's happening in their country to try to get out of responsibility for the scale of the destruction," Mr Hague said.
"We are absolutely sickened in the British Government and across the international community by what we've seen over the last few days, in particular about the deaths of more than 100 unarmed men, women and children."
He said they were "more statistics" to add to a "huge total" that demonstrate the "brutality" of the regime, adding that the deaths "illuminate the type of tyranny that the people in Syria have been experiencing".
The Syrian government flatly denied claims that its forces were responsible for the slaughter.
Foreign ministry spokesman Jihad Makdissi said that Syria was being subjected to a "tsunami of lies" and claimed that anti-government gunmen carried out the attack.
"We categorically deny the responsibility of government forces for the massacre," Mr Makdissi said.
After what was one of bloodiest episodes in the country's 14-month-old uprising, gruesome video footage emerged showing rows of dead Syrian children lying in a mosque with gaping head wounds.