At the same time, the rebel Free Syrian Army warned it would resume attacks if the government offensive does not stop.
In a statement read by US ambassador Susan Rice, the Security Council backed a demand by UN-Arab League envoy Annan for Syria to make a "fundamental change of course" to end hostilities by 6:00 am Damascus time on Thursday.
After Annan appealed for new UN backing, council members expressed "deep concern" at the Syrian government's failure to withdraw its forces and "stressed the importance that the parties meet the deadline of April 12."
Council members also "underscored" Annan's statement that "the Syrian leadership should now seize the opportunity to make a fundamental change of course," Rice said.
"It is essential that the next 48 hours bring visible signs of immediate and indisputable change in the military posture of the government forces throughout the country" as set out in Annan's six-point plan.
Washington said it hoped the Security Council would consider action if Annan concludes that Damascus broke its commitment on Tuesday's deadline.
In Moscow, Syrian Foreign Minister Walid Muallem claimed Damascus had begun carrying out the deal by withdrawing some troops out of certain provinces.
But Annan, visiting Syrian refugees in Turkey, said that while the army had indicated it was withdrawing from some areas he had received reports of troops moving into other parts of the country.
"I again appeal to the Syrian government and the Syrian parties to cease violence in accordance (with) the plan," he told reporters. "I believe there should be no preconditions for stopping violence."
Annan insisted the deal was not in tatters, however.
"The plan has not been implemented according to the schedule that we laid out... but it does not mean that it cannot be implemented."
In a letter to the Security Council, he said "the days before April 10 could have been an opportunity for the government of Syria to send a powerful political signal of peace. In the last five days it has become clear that such a signal has yet to be issued."
Fifty-two people, including 28 civilians, were killed on Tuesday, the Syrian Observatory for Human Rights said. They included 19 members of the security forces and five rebels, bringing the toll since the weekend to at least 337.
The United Nations says more than 9,000 people have been killed since anti-regime protests broke out in March 2011. Monitors put the number at more than 10,000.
Free Syrian Army spokesman Colonel Kassem Saadeddine warned that rebel forces would resume attacking regular forces if they do not withdraw.
"If (the regime) does not stop shelling and not withdraw tanks, we will intensify our military operations and launch attacks," he told AFP.
But Muallem insisted Damascus had begun implementing the Annan plan.
"We have already withdrawn military units from different Syrian provinces," he told reporters in Moscow after talks with Russian counterpart Sergei Lavrov.
Lavrov said Syria should be more decisive in fulfilling the Annan plan.
"We believe their actions could have been more active, more decisive when it comes to the implementation of the plan," he said.
Lavrov later spoke with Annan by phone, telling him to put more pressure on the rebels to cooperate with his initiative.
White House spokesman Jay Carney said Washington had so far only seen evidence of further "brutality and aggression" from Assad's forces.
"We would certainly hope the UN Security Council would evaluate the situation in Syria if in fact Mr Annan finds that the Assad regime has not abided by its own commitments to begin withdrawal by today," Carney said.
Paris and London spoke in equally tough terms.
"Bashar al-Assad has lied to Kofi Annan," said French Foreign Minister Alain Juppe.
"Not only has the firing of heavy weapons not ceased, not only is the freeing of political prisoners minimal compared with the scale of the repression, not only is Damascus now attacking its neighbours, but what has been presented as a withdrawal is nothing but a thinly disguised redeployment."
Britain's 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."
Annan arrived in Tehran late on Tuesday for talks centring on Iran's key regional ally, the official IRNA news agency reported.
Iran has repeated that it fully backs Assad's regime, and has lent it political and material support.
Meanwhile, Damascus was rebuked for violence that spilled over its borders on Monday, killing a Lebanese TV cameraman inside Lebanon and wounding four people in a Turkish camp for Syrian refugees.
Turkish Prime Minister Recep Tayyip Erdogan accused Syria of a "clear violation" of common frontiers, while Lebanon demanded an investigation.