A senior rebel official said 20 rebels guarding the buses were killed, as well as dozens of passengers. At least 39 people have been killed, according to Syrian state TV.
"Rebels say Damascus breached the terms of the deal, accusing the government of trying to bring out more loyalist fighters than agreed".
Before the blast, Syrian TV showed dozens of buses carrying thousands of people from pro-government areas Foua and Kafriya, and opposition areas Madaya and Zabadani, parked on the edge of Aleppo city, separated by walls.
Meanwhile residents from the Shiite villages were still waiting in insurgent territory on Aleppo's outskirts to cross into the city, the Observatory and a witness said.
The blast hit buses in the Rashidin area on Aleppo's outskirts, which had been waiting to cross from rebel-held territory into the government-controlled city itself, carrying people evacuated from two Shia villages on Friday. Only meters away, hundreds of evacuees from pro-rebels areas also loitered in a walled-off parking lot, guarded by government troops.
The Associated Press describes the aftermath of the blast, occurring in the Rashideen area, which is a rebel-controlled district outside Aleppo.
The agreement is one of several concluded in recent months that has seen Bashar al-Assad's regime take back control of areas long besieged by his forces and their allies.
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Earlier in the day, a source told Sputnik that a suicide attacker detonated a vehicle bomb in the Rashidin neighborhood of Aleppo near a convoy of buses carrying civilians evacuated from the Syrian Shiite towns of Fua and Kefraya.
The deal to evacuate the four towns is the latest in a string of such agreements through Syria's six-year civil war.
The evacuees from Madaya were expected to head to rebel-held Idlib, 30 miles (48km) south-west of Aleppo.
Last month, the United Nations described the situation in the pro-government north-western towns of Foah and Kefraya, and the rebel-held towns of Madaya and Zabadani near Damascus, as "catastrophic".
Thousands of Syrians being evacuated from four besieged towns were still stuck on the road on Saturday a day after leaving their homes, as the hard-won deal ran into trouble.
"The bus garage is small so there's not much space to move around". He said it is not clear what hinders the completion of the evacuation.
The SOHR said at least 2,100 residents, including rebel fighters, are due to be evacuated from Zabadani and Madaya and transported to Idlib.