Earlier on Sunday, Syrian state news agency had reported that Jaish al-Islam, which controls Douma, the largest city in Ghouta, had reached a deal with the Syrian government to leave for rebel-held areas in northern Syria.
A total of 1,146 rebels and their families evacuated the Douma district in the capital Damascus' Eastern Ghouta countryside on Sunday evening, state news agency SANA reported.
There was no immediate confirmation from the rebels, but pro-regime newspaper Al-Watan quoted "diplomatic sources" as saying the agreement would see fighters give up heavy weapons and leave Douma for northern Syria.
It also said a Russian-led committee with representatives from Turkey, Iran and Russia, the three guarantors of the Astana peace talks who set up "de-escalation" zones across Syria, would be responsible for handing over prisoners of war jailed by the rebels.
Residents trapped inside Douma expressed fear that further foot-dragging could provoke another major government offensive, like the one that killed an estimated 1,600 people across the eastern Ghouta suburbs in February and March.
Tens of thousands of rebels and civilians have been relocated to Idlib over the past years from different parts of Syria making it one of the most inhabited regions in the country.
"They will all have to agree to the settlement in the end", the source said. The Britain-based Syrian Observatory for Human Rights, which monitors the civil war through a network of activists on the ground, also reported the evacuation.
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Russian Federation is a key backer of Assad and supported the latest government offensive.
The withdrawal, the first of its kind from besieged Douma, involves fighters of Failaq al-Rahman, which evacuated most of the towns under its control inside the enclave last Saturday.
The once bustling commercial hub was the main centre of street protests in the Damascus suburbs against President Bashar al-Assad's rule that ignited the conflict seven years ago.
"This has happened within the framework of agreements reached through the mediation of Russian Federation between the Syrian army and the militants in Douma, first of all with the Jaysh al-Islam", the source said.
The unit of the powerful Lebanese Shia militia that has been fighting with the Syrian army said among the terms of the deal was setting up a Syrian government-approved local council to run the city's affairs after rebels withdraw. He said USA -led forces have increased their presence along the front line opposite the Turkey-led forces.
"Turkey will not hesitate to use initiative if terrorists in Manbij are not driven away", a statement on President Recep Tayyip Erdogan's presidential website last week read, warning the USA whose special forces there in the northern Syrian town continue to work with Kurdish-led groups.