Update 3pm: Several buses being used to free people from rebel-held villages in Syria have reportedly been attacked.
The vehicles are trying to withdraw 2,000 ill and injured people, in return for a similar number from east Aleppo.
The Syrian Observatory for Human Rights says some vehicles have been burned.
Meanwhile the UN Security Council will vote later on a French proposal to send independent observers to monitor the operation in Aleppo.
Update 11am: Buses have started entering eastern Aleppo to resume the withdrawal of civilians and wounded from the besieged Syrian city.
Aid charities are supervising the evacuation, which ground to a halt on Friday because of a disagreement with pro-government forces.
Thousands of people are left in Aleppo, some sleeping on the streets in freezing temperatures.
Activists sprinting away from Aleppo into rebel-held territory at a crossing point have filmed their terrifying ordeal.
Bassel Ibrahim and Mohammad Moustafa fled the city with hundreds of others on Friday. Gunshots could be heard ringing out across the crowded street, injecting more panic into the already fraught escape.
As they run, one of the men describes the scene, saying “these people who are being threatened by the regime are running right now at the crossing.” He adds “Hurry! Hurry! They are going to shoot. Get out” as shots are heard in the background.
According to the activists, the incident took place at a crossing point in the east of the city.
The evacuation was suspended the same day after a report of shooting at a crossing point by both sides of the conflict. It isn’t yet clear if the video shows this incident, or another.
Thousands were evacuated before the process was suspended, but estimates of citizens left in the city range from 15,000 to 40,000.
The International Committee of the Red Cross says it hopes to carry on getting people out of the besieged city very soon.
The United Nations Security Council will vote later on whether or not to send in observers to monitor the humanitarian situation.
Syrian government forces, backed by Russian allies, have taken nearly all remaining rebel-held parts of Aleppo amid reports of civilian killings.
'My soul is torn out more with each step away from Aleppo'
Those who have been able to leave Aleppo have told of their pain at being forced to leave their homes.
Modar Sheikho lost his sister to government bombing early in the revolt, and his brother was killed last month. As they looked for a place to bury him, another air strike killed his father.
Still, Sheikho held out in the besieged city as long as he could. When he finally was forced to evacuate on Friday, he made a video bidding farewell to the city.
"We were asking for our freedom. This is what we get," he said against a backdrop of bombed-out buildings and thousands of people waiting for buses to take them away from Aleppo.
But even in his first hours of exile, the 28-year-old nurse longed to return.
"My soul is torn out more with each step away from Aleppo," he whispered in an audio message to The Associated Press, not wanting to wake other evacuees in their temporary home in a village west of the ancient city.
He and thousands of others held tight to their crumbling enclave despite a gruelling four years of war.
Bit by bit over three weeks, the government offensive chipped away at their last refuge.
Their realm of destroyed buildings and crater-filled roads in eastern Aleppo shrank from 17 square miles to just one over a few weeks as forces loyal to President Bashar Assad swept through, neighbourhood by neighbourhood.
The promise of boarding buses to safety was a relief.
But for many like Sheikho, losing Aleppo was inconceivable.
Haunted by the destruction of their city
Of the more than half-dozen residents and activists that the AP has maintained regular contact with in recent months, only one said he felt disillusioned with the rebellion.
"This revolution is one of the biggest failures in the world," said 21-year-old Ahmed, who has not left the enclave yet and refused to give his family name out of fear of reprisal.
"If God saves me from this, I will go to Turkey and start a new life, away from the criminal regime and the deceiving rebels."
Most seemed haunted by the city's struggle, saying they cannot let go of their dream to create a Syria without Assad.
They said they will continue their anti-government activities somehow from wherever they end up.
One gynaecologist who had refused to leave her patients said her husband forced her to flee to a government-controlled area for safety.
The woman, who identified herself only as Farida to protect her family, had earlier sent her daughter out with thousands of other evacuees.
Farida said she could not stand living for even two days in the government-controlled sector and fled to the countryside, where the rebels are in control.
"Despite how hard it was under siege and bombardment, I was at peace with myself," she said.
Farida's husband, also a doctor, followed.
But she is still angry at him for forcing her to leave, adding: "I can't continue my life with him."
"I can't feel any joy when my colleagues are getting slaughtered," she said in text messages. She hopes to be reunited one day with her daughter.
Sheikho left on the first day of the evacuation, which was monitored by the Red Cross.
He and thousands of other holdouts boarded green government buses with portraits of Assad in the windscreen and were taken to rebel-controlled areas.
"It is very painful that I separate from my city of 28 years," Sheikho said. "I hope it is quickly liberated so I can return to it."
Besides seeing his city crumble, Sheikho watched his family shattered by more than five years of civil war.
On the first day of the government's big ground offensive three weeks ago, Sheikho and his family sought a new home to avoid intense bombing.
Like many others, his family was caught on the road by the bombardment, and his brother was killed on the spot.
He and his father had to search for a cemetery because Aleppo was running out of burial space. In the process, his father - a prominent professor of Arabic - was also killed.
Four years earlier, an air strike killed his sister outside the hospital where she worked as a nurse.
After mourning his father and brother, Sheikho had told the AP: "We are all on the road to death. May God accept them as martyrs."
Before he boarded the bus, he roamed the few streets of Aleppo still open to him for one last time - but he could not visit the graves of his relatives because the government had seized the neighbourhood where they are buried.
"I hope they forgive us" for losing Aleppo, Sheikho said.
He said he plans to be reunited with his wife, who left as the fighting intensified, and also wants to see his English teachers again.
Most likely, he will settle in a town on the Orontes River in Idlib province where rebels are in control.
Many predict that Idlib may be the next front in a government offensive.
Asked what he expected in his new life, he said: "It is the unknown future filled with painful memories."