Buses started entering several areas of Aleppo under the supervision of the Red Cross after the evacuation operation was suspended on Friday
Convoys of buses set to evacuate people from two besieged villages in Syria have been attacked, say reports.
The Syrian Observatory says some of the vehicles moving people from Al Foua and Kefraya have been burned.
Some buses, as well as Red Crescent vehicles, reached the entrance to the villages.
The coalition of forces fighting for the government of President Bashar al-Assad are demanding people to be allowed to leave the two villages in exchange for allowing evacuations of rebels and civilians from east Aleppo.
The stand-off has meant the evacuation operation has been suspended since Friday.
Meanwhile, the head of NATO Jens Stoltenberg has said western intervention in Syria would make matters worse.
The 28 NATO members belong to the US-led coalition fighting IS but they are not directly involved in the conflict in Syria.
Mr Stoltenberg said there were times where military intervention is necessary but Syria was not one of them
He told German newspaper Bild am Sonntag: "We are experiencing in Syria a horrible human catastrophe. Sometimes it is right to deploy militarily - such as in Afghanistan.
"But sometimes the costs of a military operation is higher than its benefit. Looking at Syria, NATO partners came to the conclusion that a military deployment would only make a terrible situation worse.
"We would risk turning it into a bigger regional conflict. Or more innocent people could die. A military deployment is not always the solution."
Buses started entering several areas of Aleppo on Sunday under the supervision of the Red Crescent and International Committee of the Red Cross after the evacuation operation was suspended on Friday.
The main obstacle to the resumption of the operation had been a disagreement over the number of people to be evacuated in parallel from two Shia villages, Al Foua and Kefraya, under rebel siege in northwestern Syria.
An official said: "In a first step, half of the people besieged in Aleppo will leave, in parallel with the evacuation of 1,250 people from Al Foua."
The UN Security Council will vote Sunday on a French proposal to send observers to Aleppo to monitor evacuations and report on the protection of civilians.
The council will decide on the draft resolution, despite resistance from Russia, Syria's ally and a veto-wielding Security Council member.
France said the council is "alarmed" by the worsening humanitarian crisis in Aleppo and by the fact that "tens of thousands of besieged Aleppo inhabitants" are in need of aid and evacuation.
This week Syrian forces moved to assert full control over the east of the city, which had been held by opposition fighters since 2012.