A group of stranded fighters from another insurgent group, Failaq al Rahman, who had fled to Douma from advancing army troops at the start of the latest campaign, left the city on Sunday, state media said.
The retaking of eastern Ghouta would mark a major milestone in President Assad's efforts to regain control of territory seized by rebel factions during Syria's seven-year civil war.
Douma is the last rebel-controlled town in East Ghouta, a collection of rural, working-class suburbs east of Damascus.
A civilian committee taking part in the negotiations with Russian Federation said a deal had been agreed "to evacuate humanitarian cases to northern Syria".
Later on the same day, the head of Jaish al-Islam's political office, Yaser Dilwan, said that negotiations were ongoing and seemed optimistic, but did not offer any details other than to say that different options were suggested. The Syrian Observatory for Human Rights monitoring group also reported the rebels' leaving Douma.
This photo released by the Syrian official news agency SANA, shows Syrian government forces overseeing the evacuation by buses of the Army of Islam fighters and their families from the besieged town of Douma, just east of Damascus, Syria, Monday, April 2, 2018. It will see Russian military police enter the former rebel bastion of Douma and government institutions return, the monitor said.
The civil war in Syria has wrought much damage and killed over 350,000 people.
Approximately 450 people left Douma city on Monday in an eight-bus convoy headed for opposition-held Jarablus, in northern Syria, local activists told Syria Direct. Pro-opposition media sources reported that all of Monday's evacuees were sick and injured civilians.
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There was no immediate comment from Jaysh al-Islam.
The BBC's Martin Patience in Beirut says it is not clear whether Jaysh al-Islam's fighters want to give up their weapons, and possibly become a security force under government control, or be bussed to a rebel stronghold in northern Syria.
Jaish al Islam counts around 10,000 fighters, according to SOHR.
Backed by Russia, Assad's forces have scored a series of victories over rebel forces in recent years, often through campaigns of siege, aerial bombardment and ground offensives that have drawn widespread global condemnation.
Regime forces have already retaken more than 95% of Eastern Ghouta in a six-week air and ground blitz that has killed hundreds of civilians and forced tens of thousands from their homes.
Although no official statement was issued by the faction, sources told Asharq Al-Awsat that the deal "is not similar to the previous ones that involved Harasta, which was controlled by Harakat Ahrar al-Sham, or Jubar and Zamalka, which were controlled by Failaq al-Rahman".
An old woman dressed head-to-toe in black stood by a pile of suitcases, with a child wearing a winter coat and colourful backpack by her side.
At least 1,600 people have been killed following the launch of an aerial and ground offensive by Syrian forces and their ally, Russia, on February 18, to recapture what was once known as Damascus' breadbasket.