After more than three hours of private discussions, the Security Council said it would vote on the plans to send monitors in to the besieged city.
Russia’s ambassador Vitaly Churkin had earlier said that he would veto the French draft resolution unless it was changed.
He said he had presented a rival resolution that would require the Syrian government’s approval before monitors could be sent.
As he left the meeting on Sunday, however, Mr Churkin told reporters: “I think we put in some good hours of work and I think we have a good text and we’re going to vote tomorrow morning.”
The French ambassador Francois Delattre also seemed pleased.
He said the resolution would “give us collectively the tools to avoid… a situation in which, after the end of major military operations, forces including militias would commit mass atrocities”.
He also said it would “give us some leverage to try to open the way to a broader ceasefire and toward political negotiations”.
People around the world have been protesting against the situation in Aleppo, such as this boy in Thessaloniki, Greece
Israelis in Jerusalem protested against the killing of civilians in the Syrian city
People held placards reading ‘Aleppo can not be left under bombardment’ at this protest in Reyhanli, Turkey
Doctors and nurses from charity Medact gathered in London to protest the treatment of medics in the besieged Syrian city
Protesters held Syrian opposition flags in front of the UNDP office in Amman, Jordan
There were also demonstrations in front of the Reichstag building in Berlin, Germany
Syrians living in Turkey held Syrian opposition flags during a protest along Istiklal Avenue in Istanbul
In Paris, they gathered near the Iranian Embassy, protesting against Iranian involvement in the siege
Pakistani Muslim students demonstrated in Islamabad against the ongoing conflict
In the Malaysian capital of Kuala Lumpur, protesters gathered outside the Russian Embassy
Syria Solidarity Campaign organised a march through central London. Pic: @paul_pemberton
A man holds a banner as a child lights a candle in front of the Kosovo national theatre
The vote was delayed until Monday.
The new draft asks the UN’s secretary general Ban Ki-moon “to take urgent steps to make arrangements, including security arrangements in consultation with interested parties, to allow the observation by the UN and other relevant institutions of the well-being of civilians… inside the eastern districts of Aleppo”.
US ambassador Samantha Power said the council expected to back the text “unanimously” when it votes at 2pm UK time on Monday.
Iran’s official news agency IRNA said that the foreign ministers of Russia, Turkey and Iran will also meet in Moscow on Tuesday to discuss the situation in Syria.
Meanwhile, dozens of buses entered the last rebel-held parts of Aleppo on Sunday to continue the evacuation of thousands of trapped civilians and rebels.
On Thursday, convoys of people had started to leave eastern Aleppo under a deal that allowed government forces to take full control of the city but there was little progress.
The evacuation was put on hold on Friday mainly due to arguments over how many people would also be moved from two Shia villages, Al Foua and Kefraya, which are under rebel siege in Syria’s north west.
On Sunday, the buses meant to take people from those villages were attacked and set on fire.
According to the UK-based Syrian Observatory for Human Rights, a bus driver was killed in the attack and the evacuation operation was again put on hold.
Later in the day, more than 30 buses were packed with people hoping for safety and thousands more people stood in the freezing temperatures waiting for their turn.