"An agreement has been reached to resume the evacuation of Aleppo," announced Ahmad Qara Ali, spokesman for the Ahrar al-Sham faction. He said the evacuations would begin "shortly."
The Syrian opposition agreed to surrender their last foothold in the city, last week, marking the most significant victory for President Bashar Assad since an uprising against his family's four-decade rule swept the country in 2011.
It followed a punishing offensive by the government and its regional allies that drove out tens of thousands of civilians from the east of the city. It had been held since 2012 by the opposition.
The government agreed to allow the remaining residents — fighters and civilians — to leave as part of the agreement brokered by Russia and Turkey in Ankara last week.
But a dispute delayed the final round of evacuations for over 24 hours after some 20,000 civilians and fighters were bused out of the city.
Some 3,000 rebel fighters and civilians stood outside in harsh wintry conditions overnight, waiting to board what may be the last convoy out of the east. Activists circulated photos on social media of families huddled around fires amid the sleet and snow. By midday, temperatures in the city hovered around freezing.
The Britain-based Syrian Observatory for Human Rights, which monitors the conflict through a network of activists on the ground, said 60 buses were waiting to leave.
Rebels and the government traded blame for the delay.
Syrian state media said on Tuesday evening that "differences among terrorist groups" were holding up the evacuations from Aleppo and from two rebel-besieged Shiite villages in the country's north, Foua and Kfarya. The government calls all armed opposition fighters terrorists.
The rebels are supposed to allow the evacuation of the sick and wounded from the two villages as part of a cease-fire deal reached last week to ensure the evacuation of eastern, rebel-held part of the city of Aleppo.
Ward Furati, spokesman for Aleppo's Fastaqim rebel faction, said fighters in Aleppo "won't leave until the security of all the civilians has been fully guaranteed."
Opposition media activist Ahmad Primo said the government's side was demanding to complete the evacuations from Foua and Kfarya before it would allow buses out of Aleppo.
The International Committee of the Red Cross said it was prepared to facilitate the evacuations when they resume.
Spokeswoman Ingy Sedky said the ICRC had already evacuated 750 people from the twin villages. This would leave some 1,500 more requiring evacuation, according to the deal reached by rebels and the government Monday.
On Tuesday, the ICRC said it has evacuated 25,000 people from the city since operations began last week, but the Observatory says the tally is closer to 17,000.
The Observatory also said 21 buses are still waiting to evacuate the sick and wounded from the rebel-besieged Shiite villages of Foua and Kfarya.
Also Tuesday, the U.N. humanitarian aid agency said Syria's government authorized U.N. plans to send about 20 staffers to monitor evacuations from eastern Aleppo. It was not immediately unclear if the U.N. monitors would arrive on Tuesday.
Elsewhere in northern Syria, fighting between the Islamic State group on one side, and Turkish forces and Syrian opposition forces on the other, killed four Turkish soldiers, according to the state Anadolu news agency.
The report cited unnamed military sources as saying that 11 Turkish soldiers were also wounded in the fighting for the IS-held town of al-Bab on Wednesday, including one who was reported to be in critical condition. The agency reported intense clashes near a hospital in the town, saying the militants were using it as a shelter and to store arms and ammunition.
Turkey sent ground troops into northern Syria in August to support Turkey-backed Syrian opposition forces in clearing a border area of Islamic State group militants and to curb Kurdish territorial expansion.
At least 24 Turkish soldiers have been killed so far in the operation, called Euphrates Shield.
Associated Press writer Suzan Fraser in Ankara contributed to this report.
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