Canada drafted the text - part of the 193-nation assembly's attempt to break the deadlock over Syria at the security council.
Russia and China both vetoed a draft Security Council resolution this week, calling for a seven-day ceasefire in Aleppo, the Syrian city that is on the verge of falling to regime forces.
It was the sixth time that Moscow - a close military ally of Syrian President Bashar al-Assad - has used its veto in the council to block action over Syria.
The general assembly is expected to adopt non-binding text that demands a "complete end to all attacks on civilians" and the lifting of all sieges.
"Sadly, I suspect it will be too little too late," UK Ambassador Matthew Rycroft said on Thursday.
The vote will "demonstrate that there is a moral majority" of countries that are "distressed that through a series of vetoes, the Security Council has failed to provide the unity necessary to change the situation in Syria".
Russia dismissed the resolution, saying it would have no impact on the ground.
"To expect that it's going to produce some kind of dramatic U-turn in the situation in Syria is unrealistic," Russian Ambassador Vitaly Churkin said.
UN envoy Staffan de Mistura briefed the Security Council on Thursday ahead of talks in Geneva on Saturday between the US and Russia on a possible deal that would allow civilians and rebel fighters to leave Aleppo.
French Ambassador Francois Delattre expressed support for the Canada-led push for a ceasefire, saying "it is never too late to save lives, to assist populations in need, and to lay the groundwork for a political solution in Syria".
"The fall of Aleppo will not resolve the crisis in Syria," he added.
Syria's conflict erupted in March 2011 with widespread demonstrations but has since turned into a brutal multi-front war drawing in world powers.
Many Western countries cut ties with Damascus in 2011 and some imposed crippling economic sanctions on the Syrian regime.
More than 300,000 people have been killed since the conflict began, and over half the population has been displaced, with millions becoming refugees.
The general assembly will meet from 10am [3pm GMT] to consider the draft resolution.
Agencies contributed to this report.