This "achievement exposed the size of the international conspiracy to divide Syria at the expense of the Syrian people," said MP Hasan Fadlallah after Hezbollah’s Loyalty to the Resistance bloc weekly meeting on Thursday.
Aleppo is Syria’s largest city and former commercial heart.
A convoy carrying the first evacuees from Aleppo left the city on Thursday under an exit deal.
The convoy was led by vehicles from the International Committee of the Red Cross and the Syrian Arab Red Crescent, followed by ambulances and then green government buses.
The first people to leave were the wounded and sick, and their relatives.
The deal was supposed to begin on Wednesday morning and was expected to be implemented throughout Thursday and possibly into the coming days.
The evacuation comes after a month-long army operation to recapture all of east Aleppo, a rebel stronghold since 2012.