A rebel representative told AFP an agreement had been reached to allow more people to leave the city which has been ravaged by some of the worst violence of the nearly six-year war that has killed more than 310,000 people.
But there was no confirmation from President Bashar al-Assad's regime or its staunch allies Russia and Iran, which are under mounting international pressure to end what US President Barack Obama denounced as the "horror" in Aleppo.
The UN Security Council was set to meet at 11:00 am (1600 GMT) on Sunday to vote on French proposals to dispatch monitors to oversee evacuations and report on the protection of civilians, but faced resistance from veto-wielding Russia.
French Ambassador Francois Delattre said an international presence would prevent Aleppo from turning into another Srebrenica, where thousands of Bosnian men and boys were massacred in 1995 when the town fell to Bosnian Serb forces during the Balkan wars.
"Our goal through this resolution is to avoid another Srebrenica in this phase immediately following the military operations," Delattre told AFP.
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Families spent 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 on Friday, an AFP correspondent reported.
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.
Trading accusations
The government blamed rebels for the suspension of the evacuation which began on Thursday, saying they had tried to smuggle out heavier weapons and hostages.
The opposition accused the government of halting the operation to try to secure the evacuation of residents from Fuaa and Kafraya, two villages under rebel siege in northwestern Syria.
In return, the rebels want the evacuation of the towns of Madaya and Zabadani in Damascus province which are besieged by the regime.
Al-Farook Abu Bakr, of the hardline Islamist rebel group Ahrar al-Sham, said a deal had been reached for evacuations to resume."There will be evacuations from Fuaa and Kafraya, as well as Madaya and Zabadani, and all the residents of Aleppo and the fighters will leave," he said.
The green government buses that managed to evacuate hundreds before the suspension by the Syrian government. Source: AAP
But the government did not announce any deal.
UN envoy Staffan de Mistura estimated that as of Thursday around 40,000 civilians and perhaps as many as 5,000 opposition fighters remained in Aleppo's rebel enclave.
A Turkish official said 90 wounded from Aleppo have crossed into Turkey for treatment since Thursday.
Before evacuations were suspended around 8,500 people, including some 3,000 fighters, left for rebel-held territory elsewhere in the north, said the Syrian Observatory for Human Rights.
Women, children trapped
Tens of thousands of civilians had already fled opposition-controlled parts of Aleppo after the regime began its assault in mid-November.
The Russian defence ministry said after evacuations were suspended that only hardline rebels remained.On Friday, a convoy of evacuees that had already left east Aleppo when the operation was suspended was forced to turn back.
A young boy and his family were one the lucky ones who managed to leave the city before the evacuations were suspended. Source: AAP
The International Committee of the Red Cross, supervising the evacuations, said it was looking into reports of shooting before the convoy was turned around.
The main regional supporters of the rival sides in Syria's devastating civil war engaged in a flurry of diplomacy to try to secure a resumption of evacuations.
Turkish Foreign Minister Mevlut Cavusoglu, whose government is a key backer of the opposition, said he had spoken more than a dozen times with his Iranian counterpart, Mohammad Javad Zarif, on Friday.
The official Iranian news agency IRNA later said the foreign ministers of Russia, Turkey and Iran would meet Tuesday in Moscow to discuss the Syria conflict.
Obama called Friday for impartial observers to monitor efforts to evacuate civilians, and warned Assad he would not be able to "slaughter his way to legitimacy".
Hundreds attend a rally in the UK to call for an end to the bombings in Aleppo and support civilians. Source: AAP