Syrian government forces appear to have ignored a proposed UN-sponsored ceasefire deadline and have shelled towns and villages across the country, activists have said.
Even as foreign minister Walid al-Moualem claimed it had begun withdrawing troops from Syrian cities, violence was reported in several locations.
The French foreign ministry said the Syrian ministry was guilty of a "blatant and unacceptable lie".
British foreign secretary William Hague said: "There is no evidence so far that the Assad regime has any intention of adhering to any agreement it makes.
"We will be ready to intensify our support for the Syrian Opposition, and to support others seeking to do the same. And we will begin the process of seeking the referral by the Security Council of the situation in Syria to the International Criminal Court."
Mortar fire was reported in Hama and in the northern village of Marea on Tuesday, while tanks were said to be seen on the streets of Douma.
The London-based Syrian Observatory for Human Rights said President Bashar al-Assad's forces shelled civilians in the northern area of the country after the deadline was passed.
The government had agreed to withdraw its forces from civilian areas by Tuesday under the plan drawn up by UN and Arab League special envoy Kofi Annan.
It was hoped that a full ceasefire would be in place within 48 hours.
But fierce fighting on Monday, which saw 150 people reported killed and shots fired across Syria's borders with Lebanon and Turkey, left the plan in virtual ruins.
Two people were killed in the Turkish refugee camp according to most reports, and a Lebanese journalist was also shot dead.
UN Secretary General Ban Ki-moon said he was "alarmed" by the shootings across the Turkish border, and had spoken to the foreign minister.
"The Secretary-General strongly deplores today's fatal cross-border shootings from Syria into Turkey, as well as into Lebanon," he said.
More than 24,000 Syrians have crossed the border into Turkey since the year-long uprising descended into widespread violence, activists have said.
Meanwhile in the town of Latamna dozens of people were reported killed after a residential building was hit by a shell.
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The Syrian foreign minister Walid Muallem was in Russia on Tuesday for talks as its ally was said to be growing frustrated with the lack of progress.
At a meeting in Moscow with Russian foreign minister Sergei Lavrov, Muallem said "despite all [our] positive measures we noticed on a daily basis the escalation of opposition by the armed terrorist gangs".
Lavrov said Syria could have been more "resolved" in its peace efforts, but said the opposition also needed to do more.
China also reiterated its calls for both sides of the conflict to agree to and implement a full ceasefire.
Both Russia and China had previously vetoed UN resolutions calling for Assad to leave office but had agreed to help implement the Annan peace plan.
UN and Arab League special envoy Kofi Annan will reportedly visit the camps in Turkey for a "few hours" ahead of a trip to Iran on Tuesday, a diplomatic source told Al Jazeera.
Elsewhere Iran claimed Syria had "overcome" the crisis successfully.
"Iran strongly supports the Syrian people and the reforms carried out by the Syrian leadership," said Iranian foreign minister Amir Abdullahian according to Syrian state media.
According to the UN more than 9,000 people have been killed in Syria since the uprising against Assad's government began in March 2011.