Dozens of buses began entering the last rebel-held parts of Aleppo on Sunday to resume the evacuation of thousands of increasingly desperate trapped Syrian civilians and rebels.

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 on Sunday 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.

The main obstacle to a resumption had been a disagreement over the number of people to be evacuated in parallel from two Shiite villages, Fuaa and Kafraya, under rebel siege in northwestern Syria.

A rebel representative told AFP on Sunday 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.

In New York, the UN Security Council was set to meet at 1600 GMT on Sunday to vote on French proposals to dispatch monitors to Aleppo to oversee evacuations and report on the protection of civilians.

The draft text said the council was "alarmed" by the worsening humanitarian crisis and by the fact that "tens of thousands of besieged Aleppo inhabitants" are in need of aid and evacuation.

"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.

An AFP correspondent who visited a hospital in the rebel sector saw appalling conditions with patients lying on the floor without food or water and almost no heating.

- No food, water -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.

Aleppo has seen some of the worst violence of the nearly six-year war that has killed more than 310,000 people.

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.

The International Committee of the Red Cross (ICRC) appealed for safe passage for the civilians still trapped in the city.

"People have suffered a lot. Please come to an agreement and help save thousands of lives," said ICRC Syria delegation head Marianne Gasser.

"We cannot abandon these people."

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.

On Friday, a convoy of evacuees that had already left east Aleppo when the operation was suspended was forced to turn back.

The ICRC said it was looking into reports of shooting before the convoy was turned around.

The main regional supporters of the rival sides in the devastating civil war have engaged in a flurry of diplomacy to try to secure a resumption of evacuations.

The official Iranian news agency IRNA said the foreign ministers of Russia, Turkey and Iran would meet Tuesday in Moscow to discuss the conflict.