The operation was suspended on Friday, a day after convoys of evacuees had begun leaving the rebel sector under a deal allowing the regime to take full control of the battleground city.
Buses started entering several neighbourhoods today under the supervision of the Red Crescent and the International Committee of the Red Cross (ICRC) "to bring the remaining terrorists and their families out," state news agency SANA said, referring to the rebels.
A military source confirmed to AFP that a new evacuation deal had been reached. State television said 100 buses would take people out of Aleppo.
A rebel representative told AFP today that a new agreement had been reached under which evacuations would take place in two phases from Aleppo, Fuaa and Kafraya as well as Zabadani and Madaya, two rebel towns besieged by the regime in Damascus province.
More From This Section
In New York, the UN Security Council was set to meet at 1600 GMT today to vote on French proposals to dispatch monitors to Aleppo to oversee evacuations and report on the protection of civilians.
"Our goal through this resolution is to avoid another Srebrenica in this phase immediately following the military operations," French Ambassador Francois Delattre told AFP, referring to a 1995 Bosnian war massacre.
But the proposals face resistance from veto-wielding Russia, a key backer of Syrian President Bashar al-Assad.
Families have been sheltering during the night in freezing temperatures in bombed out apartment blocks in Aleppo's Al-Amiriyah district, the departure point for evacuations before they were halted.
Abu Omar said that after waiting outside in the cold for nine hours the previous day, he had returned on Saturday only to be told the buses were not coming.
"There's no more food or drinking water, and the situation is getting worse by the day," he said, adding that his four children were sick because of the cold.
Dozens of trucks with humanitarian aid crossed the Turkish border Saturday into Syria, piling supplies in a buffer zone.