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 this week vetoed a draft Security Council resolution calling for a seven-day ceasefire in Aleppo, the Syrian city that is on the verge of falling to government forces.
It was the sixth time that Moscow, a close 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," British Ambassador Matthew Rycroft said 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 United States and Russia on a possible deal that would allow civilians and rebel fighters to leave Aleppo.
WATCH: Drone footage of the destruction of Aleppo's Old City
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.
The General Assembly will meet from 10 am (1500 GMT) to consider the draft resolution.
WATCH: SBS reporter Luke Waters sat down with Assad in July
