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Around 34,000 people have been evacuated from eastern Aleppo in a week-long rescue operation, the International Committee of the Red Cross (ICRC) said.
Over 4,000 rebel fighters were evacuated between Wednesday and Thursday to rebel-held western rural Aleppo "in one of the last stages of the evacuation," a spokeswoman said.
"The evacuation will continue for the entire day and night and most probably tomorrow (Friday). Thousands are still expected to be evacuated," she added.
All hospital patients in eastern Aleppo has been evacuated, the International Committee of the Red Cross said.
In a tweet, the ICRC wrote: "The last hospital in Eastern #Aleppo is now empty. All patients have been evacuated, along with other people in need of urgent medical care."
Thousands of Syrian civilians were left waiting in falling snow after the evacuation from the rebel-held area of Aleppo stalled on Tuesday.
The evacuation began again on Wednesday and a local news service, run by the Lebanese group Hezbollah, claimed the operation would be completed by the end of the day.
The last buses meant to evacuate rebels and civilians from Aleppo have started moving again, having been delayed by 24 hours, a UN official has said.
Earlier on Wednesday the British-based Syrian Observatory for Human Rights said 60 buses which would carry the remaining 3,000 evacuees had been halted.
The Observatory also said 21 buses were waiting to evacuate the sick and wounded from the rebel-besieged Shiite villages of Foua and Kfarya as part of the cease-fire deal reached last week.
The last buses meant to evacuate revels and civilians from Aleppo have been delayed by 24 hours, Syrian activists said.
Some 60 buses to carry the remaining 3,000 evacuees are waiting to leave Aleppo, the British-based Syrian Observatory for Human Rights said.
The Observatory also says 21 buses are waiting to evacuate the sick and wounded from the rebel-besieged Shiite villages of Foua and Kfarya as part of the cease-fire deal reached last week.
Ward Furati, spokesman for Aleppo's Fastaqim rebel faction, says the fighters "won't leave until security of all the civilians has been fully guaranteed."
The evacuations of the remaining civilians in Aleppo will be complete in a maximum of two days, Russian Foreign Minister Sergei Lavrov has claimed.
Speaking at a news conference, the minister said that Russia, Iran and Turkey had used their influence to make the evacuation happen.
It comes as the United Nations increases its presence in the Syrian city to monitor and observe the evacuations.
The evacuation of thousands of people remaining in Aleppo resumed this morning.
All sides of the conflict gave renewed security guarantees to the humanitarian organisation Syrian Arab Red Crescent and the International Committee of the Red Cross as they help with the evacuation.
The evacuation from Eastern Aleppo City will likely take several more days to complete.
Over 15,000 peoplehave so far been able to leave Eastern Aleppo City for rural areas in Aleppo and Idlib.
The UN Security Council has voted unanimously to "carry out adequate, neutral monitoring and direct observation" of the evacuations in eastern Aleppo.
The 15-member council demanded all parties in the conflict to provide UN officials and others with a "safe, immediate and unimpeded access" to those who remain in the Syrian city.
Since midnight, some 4,500 people have left the besieged rebel-held enclave of the city to surrounding villages.
The mother of a seven-year-old girl who tweeted about living conditions under the Syrian regime has spoken of her relief to finally reach safety.
Bana al-Abed attracted over 300,000 Twitter followers by providing harrowing updates on her living conditions and near-death experiences when she was growing up in besieged eastern Aleppo.
On Sunday, Bana and her mother Fatemah were some of 12,000 people to be evacuated as part of a deal to return the city to government control.
Holding her arm around her daughter, Fatemah told the activist-run Qasioun News at her relief at leaving, but also the regret of being forced out of her home city and living as a refugee.
Dozens of children who were trapped in an orphanage in the rebel-held enclave of east Aleppo have been evacuated, UNICEF said.
Geert Cappelaere, regional director for the United Nation's Children's Fund, said: "This morning, all 47 children trapped in an orphanage in east Aleppo were evacuated to safety, with some in critical condition from injuries and dehydration."
He said UNICEF and other agencies were assisting in reuniting other evacuated children with their families, and giving them winter clothes and medical care.
Some 12,000 people have been evacuated from east Aleppo in the past few days, according to Turkey's foreign ministry.
The figure includes 4,500 civilians who have managed to leave the city since midnight.
Mevlut Cavusoglu said: "Including 4,500 people in east Aleppo since midnight, 12,000 civilians in total were evacuated so far to the area under control of opposition."
The evacuations are the result of intense negotiations between Turkey - which backs some large rebel groups - and Russia, who support President Bashar al-Assad's regime in Syria.
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