The UN is preparing to send monitors to Syria to observe the implementation of a ceasefire after the first day passed without major violations.
Special envoy Kofi Annan, who brokered the ceasefire, said he was "encouraged" but Syria had not fully complied with his six-point peace plan.
Syria says it will accept UN monitors.
US Secretary of State Hillary Clinton said the ceasefire was important but was just a first step. Humanitarian groups must have full access, she said.
She also said Syrian President Bashar al-Assad would "have to go".
Security Council ambassadors have all given their support to Mr Annan's request for the rapid deployment of observers to Syria.
French Foreign Minister Alain Juppe says a draft resolution will be presented later on Thursday.
The BBC's Barbara Plett, at the UN in New York, says the idea is to despatch a small team of 20 or 30 unarmed monitors, to determine whether conditions will permit a full mission.
Mrs Clinton said the US supported the deployment of an advance team immediately.
But she said the group, as well as any full monitoring mission, "will need complete freedom of movement, unimpeded communications, and access throughout the country and to all Syrians, as well as firm security guarantees from all parties."
The Syrian opposition has called for major demonstrations on Friday.
The ceasefire, the central element in Mr Annan's plan, formally came into effect at 06:00 (03:00 GMT) on Thursday morning.
Both sides reported violations. The opposition said three people were killed in the cities of Idlib and Hama, while the Syrian government said one person died after a roadside bomb exploded in Aleppo.
But as the day went on, there were no reports of major attacks by either side.
Syria has yet to complete its withdrawal of troops and heavy weaponry from cities, which it was supposed to have done by Tuesday.
"All parties have obligations to implement fully the six-point plan. This includes both the military provisions of the plan and the commitment to move to a political process," Mr Annan told the UN Security Council.
UK Foreign Secretary William Hague welcomed the ceasefire but warned that the Syrian authorities had repeatedly broken their promises.
"They have in the days before the announcement of this ceasefire engaged in the killing of many hundreds of people in Syria," he said.
And Turkey, which has received about 24,000 refugees from the conflict, said Syria was not abiding by the Annan plan.
"There's a six-point plan put forward by Annan... Is it being implemented? I'm not of the opinion it is being implemented," Turkish Prime Minister Recep Tayyip Erdogan told reporters in Ankara.
The UN estimates about 9,000 people have died since anti-government protests began in March 2011. In February, the Syrian government put the death toll at 3,838 - 2,493 civilians and 1,345 security forces personnel.