A local council for Douma would be formed with the approval of the central government, said the government-linked Central Military Media outlet.
The Saudi-backed group, which has deep roots in the region, has held firm in recent weeks as virtually all the other insurgents of eastern Ghouta have reached deals to relocate to the rebel-held north, leaving Douma as the only remaining rebel holdout.
The head of the Britain-based Syrian Observatory for Human Rights, Rami Abdurrahman, said the Army of Islam is divided over whether to evacuate Douma, with hard-liners demanding they stay and fight.
And, while Failaq a-Rahman maintains close ties with the rebel factions that rule the Syrian northwest, including the hardline Hay'at Tahrir a-Sham (HTS) coalition, Jaish al-Islam does not.
State media has said Jaish al-Islam had accepted a deal giving its fighters safe passage to towns that are located in a buffer zone on the border with Turkey that is controlled by the Turkish military and allied Syrian rebel groups. There was no comment from the Army of Islam.
The girls tweeted that they are now in Turkey, away from danger, and hope to see all children of Syria live in peace and safety. Evacuations should be voluntary but in some cases might not have been, he added.
Dozens if not hundreds of residents are believed to require care for war wounds and medical conditions exacerbated by the siege of the town.
In Syria, the mass evacuation of civilians is threatening to leave aid workers "overrun" and "acutely underfunded", as details emerge of the unparalleled destruction in urban areas like the former ISIL-held city of Raqqa, UN senior adviser Jan Egeland has said.
Local activists say over 100,000 civilians are trapped inside Douma, which suffered devastating damage during the latest government assault.
A Syrian soldier stands at one of the underground tunnels under the recently-captured Jobar town in the Eastern Ghouta, in the countryside of Damascus, Syria.
Saif told Reuters the civilians who met the Russian and Syrian military officers had expressed concern that a departure of rebel fighters would leave them vulnerable to attack by jihadists from Nusra Front or Islamic State.
The group, which is estimated to have many thousands of fighters, has previously insisted it will not leave Douma or accept "forced displacement" to another part of Syria.