However, the Syrian Observatory for Human Rights monitoring group on Tuesday said the reports were false.
Also, SANA reported that fighters alligned with another rebel group, Faylaq al-Rahman, left Douma in buses sent by the Syrian government on Sunday.
A Syrian military source was quoted as saying that some of the fighters were rejecting the deal.
More than 45,000 rebels and their families have been evacuated from eastern Ghouta since March 22 to be relocated in Idlib, according to Syrian authorities.
There was no immediate comment from the Army of Islam.
Jaish al-Islam has not yet confirmed the accord, amid reports hardliners within the group were refusing to leave their positions.
The Syrian conflict began when the Baath regime, in power since 1963 and led by President Bashar al-Assad, responded with military force to peaceful protests demanding democratic reforms during the Arab Spring wave of uprisings, triggering an armed rebellion fuelled by mass defections from the Syrian army.
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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.
Also on Sunday, Syrian troops and allied fighters from popular defense groups were deployed to Arbin, located 9 kilometers east of Damascus, after the last group of militants left the town toward militant-held areas in northern Syria.
Local activists have said that over 100,000 civilians were trapped inside Douma, which suffered devastating damage.
The government lost control of Douma, the largest urban centre in the eastern suburbs of Damascus, in the early phase of Syria's civil war, now in its eighth year.
A journalist who was at the meeting, said that after the meeting the three leaders expressed their increase in hope for peaceful solution in the Syrian crisis in light of the latest achievements after their trilateral talks.
On Wednesday, the leaders of Russian Federation, fellow regime supporter Iran and rebel-backer Turkey are to meet for a summit devoted to Syria.
A convoy of vehicles carrying civilians from eastern Ghouta to Al Bab district are seen in Aleppo in Syria on April 03, 2018. The assault on Eastern Ghouta since mid-February has killed more than 1,600 civilians and caused tens of thousands to flee into regime-held territory.