Douma is the only town on the eastern outskirts of the Syrian capital still held by rebels, after government forces captured all other opposition areas they had besieged for years.
Earlier on Monday, the group, the last in control of territory in eastern Ghouta, said on Sunday it would not withdraw to other opposition-held parts of Syria as other rebel groups have done under deals negotiated with Syrian government ally Russian Federation.
Jaish al-Islam is also now negotiating with Russian Federation over the future of the area and the people in it.
Military sources told the media that Jeish al-Islam has not accepted the army's demand yet, and the armed forces are preparing to launch an offensive on the city if the terrorists continue to refuse leave the town and pass its control over Damascus.
Al-Watan quoted Syrian legislator Mohammed Kheir Seiryoul, who is originally from Douma, as saying that the understanding could lead to an agreement to dissolve the Army of Islam.More news: BJP is trying to change Ambedkar's Constitution, says Rahul Gandhi
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A Russian official, Stanislav Gadzhimagomedov, said the group was in touch with Russian officers handling the negotiations. The army has gained control over 90 percent of Eastern Ghouta and Douma is the only town in the Northern parts of the region that is still under the terrorists' occupation.
Al Jazeera's Zeina Khodr reports from neighbouring Lebanon.
More than 114,000 people have left Eastern Ghouta through humanitarian corridors since the declaration of a pause in hostilities, the Russian Center for Reconciliation in Syria said on Monday.
As part of the evacuation deals reached for Ghouta, rebels have released just 21 people, including civilians and soldiers, in recent days. "This sped up the regime's advance".