The rebels in Idlib released four children and eight women they kidnapped from Kafraya and Foa, and returned the bodies of eight government forces men in exchange of the release of 19 rebels detained by the pro-government fighters in Kafraya and Foa.
"It is a staggered movement of population", Abdel Hamid said.
A civilian who was travelling in one of the evacuation buses from the rebel-held towns of Madaya and Zabadani said the operation began at around 6:00 am (0300 GMT).
More than 320,000 people have been killed in Syria since the conflict began with anti-government protests in March 2011.
But residents in Zabadani and Madaya said conditions in their two towns had become too hard to bear.
Residents leaving Fouaa and Kefraya will be taken to government-held areas in Aleppo.
"The first buses that moved were the ones leaving Idlib province".
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But access has been limited, with food and medical shortages causing malnutrition, illness and even death among besieged residents. It is not clear if nearby Zabadani, included in the deal, is also being evacuated.
Some 4.7 million people live in hard-to-reach and besieged areas in Syria, including 644,000 in UN-declared besieged locations. She refused to leave her home and her land. "As long as it's temporary, we wouldn't worry about it".
If the evacuations are completed, they would be the first in number of rounds stretching over two months to evacuate some 30,000 Syrians from besieged areas, in a deal struck by rebels and the government.
The opposition said the deal amounted to a forced demographic change to displace opponents away from the main cities in western Syria.
Earlier in April, thousands of rebel fighters and their families were evacuated to the Idlib province as thousands of people from the Shia towns of Foua and Kefraya headed to regime-held parts of Aleppo.
The Syrian Observatory for Human rights confirmed the beginning of the evacuation.