The army said it had brought "security and safety" to Aleppo, ending four years of rebel resistance in parts of the northern Syrian city.
The last group of rebels and their families holed up in a small eastern enclave were evacuated on Thursday, under a deal that gives the army and its allies full control of the city after years of fighting, Syrian state television said.
At least 34,000 people, both civilians and fighters, have been evacuated from east Aleppo in a week-long operation hampered by severe winter weather, the latest U.N. figures show. But the United Nations estimates that thousands more remain.
"The process for evacuation was traumatic, with crowding, and vulnerable people waiting for hours and exposed to sub-zero temperatures," U.N. spokesman Farhan Haq told reporters in New York.
The last evacuees left a tiny pocket that was all that remained of a rebel sector that covered nearly half the city before being besieged in the summer and hit by intense air strikes that reduced swathes of it to rubble. As the months of bombardment wore on, rescue and health services collapsed.
A senior United Nations official warned that those evacuated from Aleppo after the crushing government offensive could suffer the same fate in their new place of refuge outside the city.
"Many of them have gone to Idlib, which could be in theory the next Aleppo," U.N. Special Envoy Staffan de Mistura said in Geneva.
He said a cessation of hostilities across Syria was vital if another battle like the bloody struggle for Aleppo was to be avoided.
Thousands of refugees from Aleppo were taken to Idlib, arousing fears that the rebel-held city in northwestern Syria could be next. Assad has declared that the war is far from over and that his armed forces would march on other rebel-held areas.
Assad said earlier that retaking Aleppo was a victory shared with his Russian and Iranian allies.
In comments after meeting a senior Iranian delegation, Assad said his battlefield successes were a "basic step on the road to ending terrorism in the whole of Syria and creating the right circumstances for a solution to end the war".
Russia's air force conducted hundreds of raids that pulverized rebel-held parts of Aleppo while Iranian-backed militias, led by the Lebanese group Hezbollah, poured thousands of fighters into the city.
Defense Minister Sergei Shoigu said Russian air strikes in Syria had killed 35,000 rebel fighters and halted a chain of revolutions in the Middle East.
Fighters and civilians were evacuated overnight and on Thursday from east Aleppo to opposition-held areas under an agreement between the warring sides, the International Committee of the Red Cross said.
"Most are heading toward camps, or to their relatives, or shelter locations," said Ahmad al-Dbis, a medical aid worker heading a team evacuating patients from Aleppo. "The humanitarian situation in northern Syria is very difficult, because the area is already densely populated since it has people displaced from all over Syria."
Those leaving Aleppo were not only going to Idlib, a city and province southwest of Aleppo, but to villages in the countryside in Aleppo province that lies west and north of the city and has also been heavily bombed.
Hundreds of other people were also evacuated from two villages besieged by rebels near Idlib and taken to government lines in Aleppo, part of the deal that has allowed insurgents to withdraw from the city carrying light weapons.
A rebel official said a heavy snow storm that hit northern Syria and the sheer numbers involved had delayed the evacuation.
"The numbers of civilians, their cars alongside and of course the weather all are making the evacuation slow," Munir al-Sayal, head of the political wing of Ahrar al Sham, said.
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