The deal brokered by regime ally Russian Federation would see fighters with the Jaish al-Islam rebel faction leave Ghouta's main town of Douma for opposition-held territory in northern Syria, the Syrian Observatory for Human Rights said.
The reports said buses carrying members of the Army of Islam were taking people from the besieged town of Douma to Jarablus in northern Syria.
The dominant rebel group in Douma is Jaish al-Islam, which is still negotiating a deal with Russian Federation over surrender terms giving its fighters the option of leaving the enclave or making peace with the Syrian authorities.
State media said those on board were fighters and family members belonging to the Army of Islam, the largest rebel group in eastern Ghouta.
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The retaking of Eastern Ghouta would mark a major milestone in President Bashar al-Assad's efforts to regain control of territory seized by rebel factions during Syria's seven-year civil war.
At least 1,644 civilians, including 344 children, have been killed in the offensive that began on February 18 and reduced some neighborhoods to rubble, according to SOHR, which monitors the seven-year Syrian war through activists on the ground. Syrian activists say the group has told them it is determined to remain in Douma.
"The United States is working every day on the ground and with the worldwide community to help stabilize those areas liberated from ISIS and identify ways to move forward with reconstruction once there has been a peaceful political transition away from (Syrian President Bashar al-) Assad", the statement said.
An estimated one thousand militants of the Failaq al-Rahman radical movement - along with with their families - have left the Syrian town of Douma, a source in a security service told Sputnik on Sunday.
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It was the first organized evacuation of fighters from Douma, which has held out against government forces through 7 years of war.
Jaish al-Islam has previously said it would not leave Douma and the Syrian Observatory for Human Rights monitoring group reported divisions within its ranks. More than 11 million people - about half the country's prewar population - have been displaced from their homes, including over 5 million who are living as refugees outside Syria, according to the United Nations.
It said Russia, Iran, and Turkey - which have negotiated local settlements in different parts of Syria - would oversee the handover of prisoners held by the Army of Islam to the government. Ankara says the town is controlled by Syrian Kurdish militiamen that Turkish officials claim are "terrorists" and an extension of Kurdish insurgents inside Turkey.
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