Around 30,000 people have left the one-time opposition stronghold of east Aleppo since Thursday, including all of the wounded and sick in critical condition, the International Committee of the Red Cross told AFP.
President Bashar al-Assad's government is waiting for the end of the evacuations so it can declare the completion of the offensive to recapture the one-time rebel stronghold.
The retreat from Aleppo - which had been divided into a rebel-held east and government-controlled west since 2012 - marks the biggest victory for Assad's forces in nearly six years of civil war.
It follows a month-long army offensive and weeks of siege that killed hundreds of people and left rebels with less than 10 percent of the territory they once controlled in the city.
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Despite a snowstorm on Wednesday, the evacuations continued during the day using dozens of buses and other vehicles.
The evacuations - agreed under a Russian and Turkish-brokered deal reached last week - also faced delays as they have been plagued by repeated holdups.
Red Cross spokeswoman Ingy Sedky said the "last convoys were still waiting to be evacuated from east Aleppo", and that the operation would involve "multiple" trips.
A Syrian military source said the evacuations were progressing without any obstacles.
"The announcement of the end of the operation will take place when it is completely finished," the source told AFP.
Ahmad Qarra Ali of the powerful Ahrar al-Sham rebel group said bad weather had caused delays.
"Civilians and insurgents have not yet got on the buses," he told AFP.
'Dire' conditions for evacuees
There was no precise estimate as to the number of people remaining in the city's last rebel pocket.
During the delays, the evacuees spent hours in freezing temperatures waiting in the buses to depart, as snow blanketed Aleppo and swirled through its crumbled buildings.
"The buses are not heated. The passengers, including women, children and elderly people, are suffering from the cold. They don't have food or water," said Ahmad al-Dbis, who heads a team of doctors and volunteers coordinating evacuations.
The charity Save the Children warned that those fleeing the shrinking rebel enclave face "dire" conditions, sleeping in unheated buildings or tents in sub-zero temperatures.
It said thousands of people had arrived in rural Aleppo and Idlib over the last few days, but heavy snow was hampering efforts to give them aid.
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"The thousands of young children and babies among them are extremely vulnerable, particularly as many children are weakened and malnourished after months under siege without proper food," it said.
The delays on Wednesday appeared to be connected with a parallel evacuation of residents taking place in the villages of Fuaa and Kafraya in northwestern Syria.
The two Shiite-majority villages are under siege by the rebels, who are mainly Sunni Muslims.
Shiite-dominated Iran, another key Assad ally, was reported to have insisted on the evacuations of Fuaa and Kafraya for the Aleppo withdrawal to go ahead.
Delays in the evacuations were also reported there, but state television reported later Wednesday that four buses, and two ambulances carrying wounded, had been able to leave.
The evacuation of Aleppo's rebel sector is a pivotal moment in a war that has killed more than 310,000 people and triggered a major humanitarian and refugee crisis.
Russia, Iran, Turkey take lead
As well as handing a major victory to Assad, it has given fresh impetus to international efforts to end the conflict.
Russia, Iran and Turkey agreed this week to guarantee Syria peace talks and backed expanding a ceasefire, laying down their claim as the main powerbrokers in the conflict.
Repeated attempts have failed to resolve Syria's conflict, but UN envoy Staffan de Mistura has said he hopes to convene new negotiations in Geneva in February.
The United States, another supporter of the opposition, has for years been a key player in the diplomatic efforts but has been largely excluded from involvement in the evacuation.
With President Barack Obama in his final weeks in office, Russian Foreign Minister Sergei Lavrov on Tuesday praised the Turkey-Iran-Russia format on Syria as the "most effective" way forward.
Ankara in August began an offensive in northern Syria aimed at pushing back the Islamic State group and Kurdish militias in the border area.
On Wednesday, 14 Turkish soldiers were killed and 33 wounded in clashes with IS in Al-Bab in the military's highest single day toll of the four-month campaign.
