Syria's ally Russian Federation has been deeply involved in the process, negotiating with rebels and placing masked military escorts aboard buses leaving Ghouta.
Russian President Vladimir Putin, Syrian President Bashar al-Assad's main ally in the conflict, ordered daily five-hour ceasefires and the creation of a "humanitarian corridor" to allow civilians to leave Eastern Ghouta starting from February 28.
Syrian rebel fighters have evacuated one enclave in eastern Ghouta and reached a Russian-brokered deal to leave another, enabling Syrian government forces to regain control over most of the embattled Damascus suburb, war observers said.
The latest developments come amid reports that Syrian government forces have gained control over 90 percent of the Eastern Ghouta region.
The regime responded with a crippling half-decade siege of the enclave's 400,000 residents, sealing off access to food, medicines and other goods.
Some 110,000 people have fled into government-held territory, majority on foot or motorbike, through corridors opened up by the army and its Russian allies, according to state media. He called on the factions in Southern Syria to take action to support Eastern Ghouta, pointing out that Assad's forces military action will be directed at Daraa and Idlib after getting done with the Ghouta file.
Two deals have already seen thousands of opposition fighters, their relatives and other civilians bussed out of bombed-out Ghouta districts to Idlib, a northwestern province most of which still escapes government control.
On Monday, more than 3,600 people, including hundreds of rebels, piled into more than 50 buses to leave the Faylaq-held pocket, state television said.
"The Russians don't want an agreement for Douma that's different from other parts of Ghouta, but Jaish al-Islam wants to stay and doesn't want any residents to leave", the source said.
Jaish al-Islam would lay down its heavy weapons in exchange for government-provided water and electricity returning to the town.
The first ceasefire agreement in Eastern Ghouta was concluded with the Ahrar al-Sham terrorist group that agreed to the evacuation of up to 7,500 militants and their families from the town of Harasta.
Syria's pro-government Al-Watan daily reported similar terms and said the parties had three days to study the offer.
He added that the presence of who he described as "Mujahedin"(holy warriors) near the capital Damascus is a victory for the revolution, and it is necessary to preserve this force, represented by "Jaysh al-Islam".
More than 120,000 crossed the front lines for safety, the Russian military said Tuesday. "We couldn't even find fodder to eat".