The UN General Assembly is due to vote on a resolution that condemns the Security Council for failing to stop the violence in Syria.
The text is not legally binding but is intended to increase pressure on the Council to take action.
Russia and China have blocked attempts at the UN to impose sanctions against Damascus.
The vote follows the resignation of UN-Arab League envoy Kofi Annan, whose peace plan failed to end the bloodshed.
Announcing his decision on Thursday, Mr Annan said growing militarisation had made his job untenable, but also hit out at "continuous finger-pointing and name-calling" at the UN Security Council, which he said had prevented any consensus on action.
Correspondents say Mr Annan's decision was a clear recognition that the political process has failed.
On Thursday, activists reported further deaths across the country, including in Syria's biggest city, Aleppo, where government forces have been trying to reclaim areas seized by the Free Syrian Army (FSA).
Activists say more than 20,000 people - mostly unarmed civilians - have died in 17 months of unrest.
Text 'toned down'
The UN resolution requires only a simple majority of the 193-member General Assembly to pass.
But, unlike a Security Council resolution, it will not be legally binding.
Drafted by Saudi Arabia, which openly supports the armed rebellion against President Bashar al-Assad's rule, the text condemns the Syrian government's use of "heavy weapons" and its failure to withdraw forces from civilian areas, as demanded by Mr Annan's peace initiative.
In an attempt to maximise votes, diplomats have toned down the wording of the text by dropping an explicit demand for President Assad to stand down, according to AFP.
"The aim is to increase pressure on the Assad government. We want as many people to back this which is why some changes have been made," one Arab diplomat told the news agency.
France's UN ambassador, Gerard Araud, said it would show that Russia and China are a "tiny minority" at the UN General Assembly.
Russia and China have vetoed resolutions on the crisis three times, citing opposition to any action which might be seen as regime change imposed from outside.
"Those same countries who were pushing this resolution most actively are the countries who are providing weapons to the armed opposition groups, this is unfortunately the tragedy of the matter and something which made Kofi Annan's efforts so difficult," Russian ambassador Vitaly Churkin said.
Meanwhile, China expressed regret at Mr Annan's decision not to renew his mandate, the foreign ministry said in a statement.
"We understand the difficulty of Annan's mediation work, and respect his decision," it said, according to AFP.
Mr Annan's six-point peace plan for Syria was intended to bring an end to the fighting.
But the plan was never fully adhered to by either side and the violence has continued to escalate.
UN Secretary General Ban Ki-moon said he was in discussion with the Arab League to find a successor to "carry on this crucial peacemaking effort".
But the BBC's Jim Muir, who is monitoring events in Syria from neighbouring Lebanon, says is hard to imagine a figure with anything approaching the stature and profile of Mr Annan taking over the task, when the prospects for success are currently negligible.