Syrian rebels said they have reached an agreement with the government in Damascus on Wednesday to complete their withdrawal from Aleppo, once the country's largest city.

"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 UN said Wednesday morning the evacuation had resumed.

"Buses are now moving again from east Aleppo. We hope that this continues so that people can be safely evacuated," the UN official in Syria told Reuters by email.

By Wednesday evening local time, the International Committee of the Red Cross said it had evacuated the last hospital patients from east Aleppo.

The relief organization is supervising the evacuation of the Syrian opposition's last foothold in the war-torn city.

The ICRC said Wednesday evening all residents requiring urgent medical care have been removed as well. It said the last hospital in eastern Aleppo is now empty.

Pro-government forces struck medical facilities in east Aleppo repeatedly in their push to expel the opposition from the city this year. In November, the UN said it believed there were no more functioning medical facilities in the eastern part of the city.

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Evacuations from eastern Aleppo resumed Wednesday morning after being held up for 24 hours. (Abdalrhman Ismail/Reuters)

The Syrian opposition agreed to surrender its final foothold in the city last week, marking the most significant victory for President Bashar al-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.

'Differences' held up evacuations

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 Shia 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 ceasefire deal reached last week to ensure the evacuation of the eastern, rebel-held part of the city of Aleppo.

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The last buses for the evacuation of Aleppo have been delayed, the Syrian Observatory for Human Rights says. (Ammar Abdullah/Reuters)

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 ICRC 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 Shia villages of Foua and Kfarya.