Several buses sent to transport the sick and injured from two government-held villages in Syria's Idlib province have been burned by rebels.
The attack apparently halted the latest efforts to evacuate besieged areas.
Pro-government forces say people must be allowed to leave the mainly Shia villages of Foah and Kefraya for the evacuation of east Aleppo to restart.
State media said convoys began to leave Aleppo on Sunday but other reports said they turned back.
The initial plan to evacuate the last rebel-held enclaves in the city collapsed on Friday, leaving civilians stranded at various points along the route out without access to food or shelter.
Meanwhile, the UN Security Council agreed a draft resolution on sending UN officials to monitor the evacuations in Aleppo, diplomats said. Russia, which backs the government of President Bashar al-Assad, had earlier threatened to veto the French-drafted text.
But after three hours of negotiations behind closed doors, the Security Council appeared to come to a compromise.
"We expect to vote unanimously for this text tomorrow [Monday]," said US Ambassador to the UN Samantha Power.
Buses were preparing to evacuate people from both eastern Aleppo and the government-held villages in Idlib province on Sunday.
A number of buses did succeed in entering Foah and Kefraya, according to the UK-based monitoring group the Syrian Observatory for Human Rights (SOHR), which earlier reported that Jabhat Fatah al-Sham, formerly al-Qaeda-linked Nusra Front, had been holding them up.
However, six buses were attacked and torched on the way, the SOHR said.
Syrian state media said "armed terrorists" - a term it uses for all groups fighting against President Assad - attacked five buses, burned and destroyed them.
A reporter for AFP news agency said armed men forced the drivers of the buses to get out before opening fire and setting the vehicles alight.
Several reports from opposition sources said Jabhat Fatah al-Sham was responsible. But Hezbollah's al-Manar TV and Beirut-based pro-Syrian government al-Mayadin TV said clashes between jihadist Jabhat Fath al-Sham and the rebel Islamist Ahrar al-Sham had resulted in the blaze.
The jihadist groups have not commented on the attack.
However, the Free Syrian Army, a more moderate rebel faction, condemned it as a "reckless act endangering the lives of nearly 50,000 people" in east Aleppo.
Syrian state media said buses entered eastern Aleppo around noon local time, under the supervision of the International Red Cross and the Syrian Arab Red Crescent.
Some 1,200 people were due to be taken out of the former rebel enclave in return for a similar number moved out of the two government-held villages, Foah and Kefraya.
Pro-government forces had reportedly demanded that a group of people needing medical treatment also be allowed to leave the two areas.
Reports said a new agreement was reached in the early hours of Sunday but delays meant thousands of civilians remained stranded.
Bombardment of east Aleppo has left it virtually without medical facilities. A video published on Sunday showed nurses performing a Caesarean because the siege has prevented surgeons reaching the stricken area.
Among the people waiting to leave eastern Aleppo are sick and wounded children, said the children's charity Unicef.
Some young children have been forced to leave without their parents, the charity said, and hundreds of vulnerable children remain trapped.