The evacuation of the last remaining civilians and fighters from rebel-held districts of the Syrian city of Aleppo should be completed by Thursday night or Friday, the Red Cross says.
The final phase is expected to take place over multiple stages and involve dozens of buses and hundreds of cars.
Thousands of people are still waiting to be evacuated.
The Red Cross says 34,000 have left the city since the evacuations began eight days ago as part of a ceasefire deal.
The evacuees are being taken to rebel-held territory in the countryside west of Aleppo and the neighbouring province of Idlib, where camps are being set up.
International Committee of the Red Cross (ICRC) spokeswoman Ingy Sedky told AFP news agency: "The evacuation will continue for the entire day and night and most probably tomorrow (Friday)."
"Thousands are still expected to be evacuated."
A spokesman for the rebel group Ahrar al-Sham, Ahmed Kara Ali, told Reuters news agency that "large numbers" of people were still inside the enclave, which covers about 2.6 sq km (1 sq mile).
Some 400 private vehicles, including pick-up trucks and cars, arrived overnight at the rebel-held town of Khan al-Assal, just to the west of Aleppo, a doctor involved in the operation told AFP. Ms Sedky said 4,000 people were in the convoy.
"The bad weather, including heavy snow and wind, and the poor state of vehicles mean things are moving much more slowly than expected," she added.
The evacuations had earlier been held up for more than 24 hours, forcing thousands of people to spend Tuesday night waiting outside in freezing temperatures with little to eat or drink.
The reasons for the delay were not clear. But state media blamed rebels in Idlib, accusing them of preventing buses from reaching two besieged, pro-government Shia towns that are being evacuated simultaneously as part of the ceasefire deal.
Several buses and ambulances were eventually allowed to enter and leave Foah and Kefraya on Wednesday afternoon, and Ms Sedky said another four buses would evacuate people from the towns on Thursday.
The Syrian government is waiting for the Aleppo evacuations to be completed before troops move into the rebel enclave and take full control of the city.
President Bashar al-Assad meanwhile said defeating the rebels there had been a victory not just for Syria but also for its allies, Iran and Russia.
The Syrian army broke four years of deadlock in Aleppo with the help of Iranian-backed Shia militias and Russian air strikes, reinstating a siege on the east in early September and storming the rebels' defensive lines two months later.
Also on Thursday, Russia's Defence Minister Sergei Shoigu announced that its warplanes had carried out 18,800 sorties since launching an air campaign against Mr Assad's opponents in September 2015.
In total, they had "liquidated 725 training camps, 405 weapon factories and workshops, 1,500 pieces of terrorist equipment, and 35,000 fighters", he said.
Human rights groups have accused the Russian and Syrian air forces of committing war crimes in Aleppo, alleging that they killed hundreds of civilians this September and October alone, deliberately targeted medical facilities, and used indiscriminate weapons such as cluster and incendiary munitions.