The evacuation effort has been hampered in recent days by heavy snowfall and freezing temperatures -- leaving evacuees waiting in unheated buses for hours -- but aid workers said it appeared to be reaching its end.
"We expect today to be the last convoys, the operation will continue all day long and during the night," said Ingy Sedky, the spokeswoman in Syria for the International Committee of the Red Cross.
About 34,000 people have left the one-time opposition stronghold of east Aleppo since last Thursday, including all of the wounded and sick in critical condition, according to the ICRC, which is assisting in the evacuation.
Rebel forces, who seized control of east Aleppo in 2012, agreed to withdraw from the bastion after a month-long army offensive that drove them from more than 90 percent of their former territory.
The agreement was brokered by Russia, a key ally of President Bashar al-Assad that launched air strikes in support of his regime last year, and Turkey, which supports the opposition.
Once the evacuations are complete, Assad's forces will be able to claim total control of Aleppo, in the regime's biggest victory in more than five years of civil war.
Ahmad al-Dbis, who heads a team of doctors and volunteers coordinating evacuations, said some 400 vehicles had arrived overnight Thursday in Khan al-Assal, the staging ground where evacuees from Aleppo arrive.
It was unclear how many people -- either fighters or civilians -- remained.
The heavy snowfall from the day before, which blanketed Aleppo and the surrounding countryside, had stopped but was still slowing down the evacuations.
"It is hard to say when the operation will be finished because the roads are snowed under," said Ahmad Qarra Ali of the powerful Ahrar al-Sham rebel group.
At least 750 people have been able to leave the villages in recent days, most passing through Khan al-Assal on their way to Aleppo.
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.