Some 20,000 people have been evacuated from Syria's east Aleppo so far and efforts continue to bring more people out, Turkish Foreign Minister Mevlut Cavusoglu says.
Cavusoglu had said earlier on Monday that 12,000 people had been evacuated.
Dozens of buses carrying thousands of people from Aleppo's tiny rebel zone reached insurgent areas of countryside to the west of the city, according to a United Nations official and the Syrian Observatory for Human Rights, a monitoring group.
Convoys of buses from eastern Aleppo reached rebel-held areas of countryside to the west of the city on Monday, according to a UN official and the Syrian Observatory for Human Rights, a monitoring group.
At the same time, 10 buses left the Shi'ite Muslim villages of al-Foua and Kefraya, north of Idlib, for government lines in Aleppo, the sources said.
The evacuation of civilians, including wounded people, from the two villages had been demanded by the Syrian army and its allies before they would allow fighters and civilians trapped in Aleppo to depart. The stand-off halted the Aleppo evacuation over the weekend.
"First limited evacuations, finally, tonight from east Aleppo and Foua & Kefraya. Many thousands more are waiting to be evacuated soon," Jan Egeland, who chairs the United Nations aid task force in Syria, tweeted late on Sunday night.
Syrian state TV and pro-Damascus stations showed the first four buses arriving in Aleppo from the besieged villages, accompanied by pick-up trucks and with people sitting on their roofs.
In Idlib, aid workers said more than 60 buses had arrived from Aleppo. Some evacuees were being taken in by relatives or other residents, while others could be housed in tents.
Aleppo capture doesn't mean war is ending
The recapture of Aleppo is Syrian President Bashar al-Assad's biggest victory so far in the nearly six-year-old war, but the fighting is by no means over with large tracts of the country still under the control of insurgent and Islamist groups.
Later on Monday, the Security Council will vote in New York on a resolution to allow UN staff to monitor the evacuations.
The draft resolution was the result of a compromise between Russia and France, and the United States said it was expected to pass unanimously.
On Sunday, some of the buses sent to al-Foua and Kefraya to carry evacuees out were attacked and torched by armed men, who shouted "God is great" and brandished their weapons in front of the burning vehicles, according to a video posted online.
That incident threatened to derail the evacuations, the result of intense negotiations between Russia - Assad's main supporter - and Turkey, which backs some large rebel groups.
The foreign ministers of Russia, Iran and Turkey will hold talks in Moscow on Tuesday aimed at giving fresh impetus for a solution in Aleppo.
At stake is the fate of thousands of people still stuck in the last rebel bastion in Aleppo after a series of sudden advances by the Syrian army and allied Shi'ite militias under an intense bombardment that pulverised large sections of the city.
Twitter's Bana Alabed escapes
A seven-year-old Syrian girl who captured global attention with her Twitter updates from Aleppo has been evacuated from the city, an aid organisation says.
Helped by her mother, Fatemah, who manages the @AlabedBana account, Bana Alabed has uploaded pictures and videos of life during the nearly six-year-old Syrian war, gaining around 331,000 followers on the site since September.
Last week, mother and daughter shared a video of themselves asking US First Lady Michelle Obama for help in reaching a safe place after advances by the Syrian army and allied Shi'ite Muslim militias into rebel-held eastern parts of the city.
A ceasefire and evacuation deal was agreed last Tuesday but thousands of people have struggled to leave due to hold-ups.
"This morning @AlabedBana was also rescued from #Aleppo with her family. We warmly welcomed them," Turkish aid agency IHH wrote on Twitter on Monday with a picture of the smiling young girl alongside an aid worker.
Speaking to the pro-opposition Qasioun news agency in al-Rashideen on the southwest edge of Aleppo, Fatemah said in English: "I am sad because I leave my country, I leave my soul there ... We can't stay there because there are a lot of bombs, and no clean water, no medicine.
"When we get out, we had a lot of suffering because we stayed almost 24 hours in bus without water and food or anything," Fatemah continued. "We stayed like a prisoner, a hostage but finally we arrived here."
Reuters / Newshub.