Censor.NET reports citing Reuters.
The British-based Syrian Observatory for Human Rights said the delay was because rebels from Zabadani, one of the towns included in the deal, had not yet been granted safe passage out.
The agreement is one of several concluded in recent months that has seen President Bashar al-Assad's government take back control of areas long besieged by his forces and their allies.
In the latest deal, hundreds of rebels and their families evacuated the town of Madaya near Damascus, and were taken to the government-held city of Aleppo. From there they will travel to Idlib province, an insurgent stronghold.
In return, pro-government fighters and residents from the Shi'ite villages of al-Foua and Kefraya, both surrounded by Idlib rebels, have left the area and reached Aleppo's outskirts.
Related materials: War in Syria