Douma is the last town to hold out against government forces in the once rebel-held suburbs.
Thousands of rebels, their families and other civilians have already departed other parts of eastern Ghouta for Idlib province, another insurgent-held area of northern Syria.
Russia's military also said Sunday that a preliminary agreement has been reached on the evacuation of Army of Islam fighters. Maj.
A Hezbollah run-media unit said on Sunday an agreement had been reached after several days of negotiations to spare bloodshed in Douma.
A local council for Douma would be formed with the approval of the central government, said the government-linked Central Military Media outlet.
Mr Charles Lister, a senior fellow and director of the Extremism and Counter-terrorism Programme at the Middle East Institute, noted that a sudden withdrawal of U.S. forces would immediately bolster Iran, Russia and the regime of Syrian President Bashar al-Assad.
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.
Just last week, two coalition soldiers-one American and one British-were killed by an improvised explosive device near Manbij, a city in northern Syria near the Turkish border.
The agreement brokered by government ally Russian Federation would see fighters with the Jaish al-Islam rebel faction leave Ghouta's main town of Douma for opposition territory in northern Syria, state media and a monitoring group said.
A Russian-brokered deal had been reported on Sunday for fighters with Jaish al Islam (or Army of Islam), the largest rebel group still in Ghouta, to leave the enclave's main town of Douma.
The Syrian army entered the areas that had been controlled by the Failaq al Rahman on Saturday evening after the last batch of them evacuated toward Idlib.
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The officials said the hold, first reported by The Wall Street Journal, is not necessarily permanent and will be discussed at senior-level inter-agency meetings next week.
"Jaish al Islam has taken the decision to remain steadfast and the idea of leaving is not on the table", said the official.
A Syrian military source was quoted as saying that some of the fighters were rejecting the deal.
Douma is a stronghold of the powerful Army of Islam rebel group.
Russian Federation has been a key backer of Syrian President Bashar Assad, ultimately helping to turn the tide of the devastating civil war in his favor.
Rebels have left behind a labyrinth of tunnels under Eastern Ghouta, fitted with hospitals and military headquarters, and some of them wide enough to drive a vehicle through.
Faylaq al-Rahman did not have a significant presence in the Douma.
United States and United Kingdom defense officials on Saturday released the names of the two troops who were killed this week in an improvised explosive device attack in the Manbij area of Syria.
"We're coming out of Syria, like, very soon".
No date was given for the pullout and Moscow said rebels were expected to demine buildings and clear roadblocks before leaving.
Numerous predominantly Sunni Muslim inhabitants of eastern Ghouta say they fear their displacement was part of a deliberate attempt to bring demographic changes in strategic areas that dilutes their presence in favor of Assad's Alawite sect and other minorities.