Syria conflict: 'Families leave' besieged Aleppo
The civilians boarded buses where they were taken to temporary shelters, state news agency Sana said.
Some rebel forces had also surrendered to government forces, the report said.
Russia, an ally of the Syrian government, announced on Thursday that four exit corridors would be opened in Aleppo for civilians and rebels.
The move was welcomed cautiously by the UN, the US and some aid agencies.
The US has suggested the plan may be an attempt to force the evacuation of civilians and the surrender of rebel groups in the city.
On Friday, the UN's envoy to Syria appealed to Russia to let the UN manage the corridors.
"This morning dozens of families left via the corridors identified... to allow the exit of citizens besieged by terrorist groups in the eastern neighbourhoods," Sana reported.
"They were welcomed by members of the army and taken by bus to temporary shelters," it added.
The report also said some fighters had handed over their weapons and surrendered to the authorities.
Syrian President Bashar al-Assad has offered an amnesty for rebels laying down arms and surrendering within three months.
The Sana report showed pictures of people, mostly women and children, walking past soldiers and getting onto buses.
UK-based monitoring group the Syrian Observatory for Human Rights also said that "a number" of civilians had left eastern Aleppo through a passage in the Salaheddin neighbourhood.
Source: bbc.com