That comes after Russia’s promise to veto the French resolution and its putting forward a rival draft.
The voting on the new version of the document is scheduled later on Monday, Vitaly Churkin said.
The US ambassador to the UN believes the resolution will be passed unanimously.
"We expect to vote unanimously for this text tomorrow at 9am (1400 GMT),” Samantha Power told reporters after a three-hour closed door meeting.
The French-drafted resolution for placing the Aleppo evacuation under the supervision of the UN is “dangerous and impossible to implement," Russia's ambassador to the UN said earlier, promising to veto the initiative and put some new proposals on the table instead, RT reported.
We cannot allow it to pass because this is a disaster,” Churkin said commenting on the French-initiated resolution.
“Actually, in certain situations we were disappointed that representatives of UN humanitarian agencies were not ready for the monitoring mission. We don’t have problems with any kind of monitoring. We will support appropriate UN monitoring process. But the idea that the observers would walk amid eastern Aleppo ruins without sufficient training and without giving an account of what will be going on there is a tragedy and a provocation. I hope that this is not an intended provocation,” he added.
Churkin said Russia has concrete proposals on how to arrange the work of UN observers in the safest way possible.