The BBC quoted a United Nations officials confirming that at least three hundred and fifty people left rebel enclaves late on Sunday, heading towards government territory.
However, other reports indicate that buses that sent to take people out of government-controlled areas, besieged by rebels, were set alight.
Meanwhile; the UN Security Council has agreed a compromise to allow UN monitoring of the operation.
US Ambassador to the UN SAMANTHA POWER said a unanimous vote is expected, as the Security Council meeting opens in New York
Russia had earlier rejected a French-drafted plan to send UN officials to east Aleppo as a disaster.
