The Britain-based Syrian Observatory for Human Rights announced the deal. It said the evacuation of Al Foua, Kefraya, Zabadani and Madaya might not begin before April 4, but local ceasefires have gone into effect.
Up to 15,000 people are expected to leave the city over the next couple of weeks, making this the largest evacuation plan of its kind in Syria since the start of the war.
More than 180,000 people in Marysville, Yuba, Butte and Sutter counties had left their homes after Sunday's evacuation order.
America's tallest dam is in danger of collapse, forcing hundreds of thousands to leave their homes.
Many civilians started are returning to the city for the first time in five years after the regime pushed out the rebels from eastern part of the city.
The strikes come after the last opposition fighters and civilians were evacuated from the city's eastern districts this week
With no assets, employment or anywhere to live, families who left everything behind in Aleppo are now facing a very tough future.
Regime forces warned civilians and rebels to leave the besieged opposition enclave as it prepares to move in and take full control of the devastated city.
The Turkish foreign minister said 37,500 people had already left the Syrian city and evacuations could be completed by Wednesday.
A second convoy of civilians has left eastern Aleppo, and civilians have left two Shia villages, as evacuations pick up pace in Syria.
A World Health Organization official in Syria says the evacuation process is "going smoothly".
Leaders at a European Council Summit on Thursday called for an immediate cessation of hostilities to allow humanitarian access to the war-ravaged Syrian city. TRT World's Simon McGregor-Wood reports from Brussels.
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