Evacuations have resumed from east Aleppo, with buses and ambulances leaving rebel areas of the Syrian city.
At least 350 people reportedly left rebel enclaves late on Sunday, heading towards other rebel-held territory.
Thousands more are waiting to leave east Aleppo amid dire conditions.
The UN Security Council is said to have agreed a compromise to allow UN monitoring of the operation. Russia earlier rejected a French-drafted plan to send UN officials to east Aleppo as “a disaster”.
“We expect to vote unanimously for this text,” said US Ambassador to the UN Samantha Power.
The Security Council meeting will start at 09:00 (14:00 GMT) in New York.
Initial efforts to evacuate the last rebel-held enclaves in the city collapsed on Friday, leaving civilians stranded at various points along the route out without access to food or shelter. Bombardment of east Aleppo has left it virtually without medical facilities.
Despite further setbacks on Sunday, buses and ambulances began moving out of the area after nightfall.
“Evacuations are on,” the UN official said in an email message to Reuters news agency, adding that the first people left east Aleppo at around 23:00 local time (21:00 GMT).
Five buses carrying evacuees arrived in rebel-held Khan al-Assal, the AFP news agency said, quoting Ahmad al-Dbis, who heads a team of doctors co-ordinating evacuations to the town.
From Khan al-Assal, the evacuees are expected to travel to parts of Aleppo and Idlib provinces.
In order for the evacuation of east Aleppo to restart, pro-government forces had demanded that people must be allowed to leave the mainly Shia villages of Foah and Kefraya in Idlib province, besieged by rebels.
Syrian state TV and the Syrian Observatory for Human Rights, a UK-based monitoring group, said early on Monday that 10 buses had now left the villages. The Observatory said 500 of the 4,000 villagers had left.
Earlier on Sunday, armed men set fire to at least five buses that were about to transport the sick and injured from the villages.
Several reports said the Jabhat Fateh al-Sham group, linked to al-Qaeda, was responsible.
But Hezbollah, the Lebanese militant group fighting alongside Syria’s government, said the blaze started during fighting between the jihadists and another Islamist rebel group that supported the evacuations.
The jihadist groups have not commented on the attack.
However, the Free Syrian Army, a more moderate rebel faction, condemned it as a “reckless” act that had in turn endangered the lives of thousands of trapped people in eastern Aleppo.
Among the people waiting to leave eastern Aleppo are sick and wounded children, said the children’s charity Unicef.
Some young children have been forced to leave without their parents, the charity said, and hundreds of vulnerable children remain trapped.