More than 1,600 of Eastern Ghouta's 400,000 have died since the offensive began in February.
Buses, which entered the Douma district earlier to transport the fourth batch of the Islam Army rebels and their families, had to leave the area empty to "stay away from the conflict among the Islam Army rebels", the report said.
Indicating divisions in Jaish Al Islam, a Syrian military source told Reuters some of the fighters were rejecting the deal and the army would use force unless they accepted it.
In the past 24 hours, an additional 1,100 Jaish al-Islam fighters and their families have left the town of Douma in Eastern Ghouta, Russia's defence ministry also said.
Rami Abdurrahman, the Observatory's director, said some factions within the Army of Islam oppose evacuating and effectively surrendering Douma to the government of President Bashar Assad.
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It was not immediate possible to confirm the details of the deal and there was no comment from the Army of Islam.
The deal would mark the end of a weeks-long push by the government to consolidate its control of the eastern Ghouta region just outside the capital.
An opposition official told the Saudi TV channel al-Arabiya that the Army of Islam was still engaged in talks with Russian Federation over the future of Douma. Syrian government forces responded by putting the town and other suburbs around Damascus under siege, bombing hospitals and residential areas, and blocking the entry of food and medical relief.
Al Jazeera's Osama Bin Javaid, reporting from Ankara, said that after the meeting the three leaders expressed their increasing hope for peaceful solution in the Syrian crisis in light of the achievements produced by their trilateral dialogue.
The now deserted highway was pockmarked with bomb craters and wound its way through bleak, apocalyptic scenes of neighbourhoods destroyed by years of fighting in Syria's bloody civil war.
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Also on Sunday, Hezbollah media said that an agreement had been reached with the rebel group to evacuate fighters to Jarablus, a town in northern Syria near the border with Turkey.
Russian Federation is a key backer of Assad.
The Syrian pound has appreciated around 10 per cent against the USA dollar in recent days, as rebel fighters quit their final stronghold of Eastern Ghouta on the edges of the capital.
Some 1,300 fighters, activists, and civilians signed up to leave the town, according to the Britain-based Syrian Observatory for Human Rights.
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