The Syrian Observatory For Human Rights says vehicles moving people from Al Foua and Kefraya have been burned and destroyed.
Coalition forces fighting for the government of President Bashar al Assad are demanding people to be allowed to leave the two villages in exchange for allowing evacuations of rebels and civilians from east Aleppo.
Evacuations were postponed following the bus attacks, but reports said 350 people had been able to leave the city later on Sunday.
Syrian state media reported that “armed terrorists” – a term it uses for insurgent groups fighting against Mr Assad’s rule – attacked five buses and burned and destroyed them.
Rebel officials claim an angry crowd of people, possibly alongside pro-government forces, carried out the bus attacks.
A resident in the area said it was not carried out by the group formerly known as the Nusra Front, which previously said it had not agreed to the evacuation of the two villages.
The stand-off has meant the evacuation operation has been suspended since Friday.
Syrian state media has reported that a number of fighters and their families have started to leave Eastern Aleppo.
Meanwhile, the head of NATO Jens Stoltenberg has said western intervention in Syria would make matters worse.
The 28 NATO members belong to the US-led coalition fighting IS but they are not directly involved in the conflict in Syria.
Mr Stoltenberg said there were times where military intervention is necessary but Syria was not one of them
He told German newspaper Bild am Sonntag: “We are experiencing in Syria a horrible human catastrophe. Sometimes it is right to deploy militarily – such as in Afghanistan.
“But sometimes the costs of a military operation is higher than its benefit. Looking at Syria, NATO partners came to the conclusion that a military deployment would only make a terrible situation worse.
“We would risk turning it into a bigger regional conflict. Or more innocent people could die. A military deployment is not always the solution.”
Buses started entering several areas of Aleppo on Sunday under the supervision of the Red Crescent and International Committee of the Red Cross after the evacuation operation was suspended on Friday.
The main obstacle to the resumption of the operation had been a disagreement over the number of people to be evacuated in parallel from two Shia villages, Al Foua and Kefraya, under rebel siege in northwestern Syria.
An official said: “In a first step, half of the people besieged in Aleppo will leave, in parallel with the evacuation of 1,250 people from Al Foua.”
Dozens of buses began entering the last rebel-held parts of east Aleppo on Sunday to resume the evacuation of thousands of increasingly desperate trapped civilians and rebels.