State news agency SANA said "a number of buses" carrying Jaish al-Islam fighters and their family members had exited through the checkpoint.
The buses are now waiting on the Harasta highway nearby for the militants to settle their dispute. The source said on Tuesday the government had set a deadline for militants to leave Douma, without saying how long.
The comments came on the same day the Syrian army had declared "victory" against rebel groups in Eastern Ghouta.
If confirmed, the departure of Jaish Al Islam from Douma would mark the end of the war for eastern Ghouta, wiping out an opposition stronghold near Damascus and underlining President Bashar Al Assad's unassailable position in the war.
05 de abril de 2018, 13:02Damascus, Apr 5 (Prensa Latina) The liberation of Eastern Ghouta by terrorists groups showed that the Syrian army wins in any scenario against those West-backed radical bands, stated today the Public and Media Advisor to the Presidency, Bouzeina Shaaban.
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.
Damascus:China has donated $1 million in aid to the World Food Programme (WFP) in Syria to purchase food for the war-stricken Syrians, the Chinese Embassy in Syria has said.
Over the past weeks, as Syrian forces reclaimed towns and villages in eastern Ghouta, they gave rebels and all men of fighting age the choice of accepting amnesty and serving in the Syrian military conscription, or leaving to go to the north of Syria.
The rebels and their families are taken to Idlib.
Last week, two rebel groups reached an evacuation deal with the Russian army, which resulted in about 19,000 people leaving for the northern province of Idlib.
"The joint investigation mechanism that emerged from UN resolution 2235 proves that Syrian regime forces have used chemical weapons at least three times while it was still investigating other incidents before Russian Federation ended its mission using its veto in the UN Security Council" the report said.
The government offensive in Ghouta has been one of the deadliest of the war, killing more than 1,600 civilians, according to the Observatory.