The Red Cross says it has evacuated 148 people from Aleppo's Old City.
The old city was controlled by rebels until it was retaken by the Syrian regime on Wednesday.
The evacuees, mostly elderly and disabled, had been trapped for days.
The President of the Aleppo City Council, Brita Hagi Hasan, who is linked to the opposition, says 150,000 people are still at risk.
He says at least 150,000 people have been condemned to death in the city of Aleppo and that more than 800 people have died in the past 26 days.
During that time, the Syrian regime has retaken about 75 percent of eastern Aleppo - a place that was under rebel control for the last four years.
This has triggered a mass evacuation of civilians in the area who are suffering without basic human needs, like food and water.
TRT World spoke to Ismail Abdulla who chose to stay behind and work for the White Helmets, a volunteer-based humanitarian organisation in Syria.
He said people are afraid that Aleppo may fall under regime control, and if it does, there could be a genocide.
As the fighting intensifies in eastern Aleppo, the United Nations says it hasn't been able to evacuate wounded children.
The United States and Russia are far from reaching an agreement on how to get people to safety, the UN's Syria humanitarian adviser Jan Egeland said.
TRT World correspondent Sandra Gathmann has more from Jarablus in Syria.