Families left eastern Aleppo districts via routes identified as safe passages by the Syrian authorities, Xinhua news agency reported.
The Syrian army received the families at Salahuddien district, transporting them to temporary shelters by bus.
However, some rebels were still preventing families from leaving.
On Thursday, President Bashar al-Assad offered amnesty to all the rebels who surrendered within 30 days and announced the opening of three safe exits for civilians to leave the rebel-held districts.
The move came after the Syrian army completely severed the rebel supply lines into eastern Aleppo, making them totally besieged.
Aleppo, Syria's largest province and once a thriving economic metropolis, has been witnessing violent clashes lately as the Syrian army advances against the rebels.
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