Hours after rebels had set ablaze a number of buses that were supposed to carry civilians out of Aleppo, the evacuation procedure resumed late Sunday.

Thousands of people were set to be taken out of the war-torn Aleppo this weekend under a new complex people-swap deal. However, six buses set to evacuate the loyalist areas were set on fire by rebel fighters, believed to be the Syria-based jihadist group Jabhat Fateh al-Sham.

After several hours, people from eastern Aleppo and the towns of Kefraya and Foua began to be evacuated through the first "limited evacuations." Through a Twitter post, United Nations humanitarian adviser Jan Egeland provided the update that thousands are still waiting to be evacuated.

Robert Madini of the International Committee of the Red Cross said five buses and one ambulance had left Aleppo shortly after midnight. According to medical officials, about 350 people were collected out of Aleppo after the evacuation resumed.

Ahmad al-Dbis, head of a team of doctors and volunteers coordinating the evacuations to rebel-held Khan al-Assal, said that the evacuees who were transported by five buses were in terrible state.

"They hadn't eaten, they had nothing to drink, the children had caught colds, they were not even able to go to the toilet," he added.

According to the Syrian Observatory for Human Rights, the 350 evacuees were able to be transported after Russia and Turkey urged the Syrian regime to allow the convoy of buses to pass its final control point.

Nine thousand people had already been evacuated from the rebel-besieged towns before the operations got suspended Friday.

The stalled evacuation was part of a deal to free east Aleppo's remaining civilians in exchange for sick and wounded people from two pro-government villages. The buses were intercepted in an area controlled by Jund al-Aqsa, a jihadi faction aligned to the Syrian opposition.

Initially a straightforward evacuation agreement, it has become a complicated three-stage deal involving Aleppo and four other cities.

Although some resistance to the deal was expected, cooperation from opposing parties in the Syrian civil war that has raged for more than five years is necessary.