At least 80 buses left Fuaa and Kafraya in Idlib province in the northwest, an Agence France-Presse correspondent in rebel-held territory said.
At least 100 people have been killed in the blast near evacuation buses outside Aleppo city, the Syrian opposition rescue service has said.
"Rebels say Damascus breached the terms of the deal, accusing the government of trying to bring out more loyalist fighters than agreed".
At least 39 people are dead after a auto bomb exploded near a convoy carrying evacuees from besieged areas of Syria, human rights groups and Syrian media report.
Residents of al-Foua and Kefraya, the Shia villages, were waiting in the Rashidin area. The Observatory said more than 24 were killed and scores more wounded.
Thousands of Syrians were stuck in and around Aleppo on Saturday as a deal to evacuate fighters and civilians from four towns as part of a coordinated population swap stalled, according to a monitor and activists.
The blast hit the Rashidin area on Aleppo's outskirts, where dozens of buses carrying mostly Shi'ite residents of two villages that are being evacuated in a deal between warring sides were waiting to enter the city.
Windows users should be really anxious about the latest NSA leak
However, the firm did concede to the possibility that the local messaging system of some of its clients could have been breached. In response, Swift has said there is no evidence that the main Swift network had ever been accessed without authorisation.
A media unit run by Hezbollah, which backs the Syrian government of Bashar al-Assad, said the suspected attacker detonated a vehicle bomb near the convoy of people evacuated from towns besieged by rebel forces in northern Syria. Only meters away, hundreds of evacuees from pro-rebels areas also loitered in a walled-off parking lot, guarded by government troops. He accused the government or extremist rebel groups of orchestrating the attack to discredit the opposition.
A Lebanese TV channel close to the Syrian government is airing footage showing new buses arriving at an evacuation point that was site of a major explosion that killed dozens. According to the New York Times, the evacuations were the result of a deal brokered by the Syrian government.
Prior to the blast, Syrian Red Crescent teams had distributed meals to the restless evacuees, stuck in limbo after having left their homes over 30 hours earlier.
An AFP correspondent west of Aleppo, speaking before the explosion, said the coaches carrying government evacuees had not moved in 30 hours.
"We are not moving forward or backward", he said.
A resident of Zabadani - another rebel-held town to be evacuated - Amer Burhan says no evacuation had even taken place from there. He said it is not clear what hinders the completion of the evacuation.