"There are divisions among the Jaish al-Islam group on their leaving but we are continuing preparations", the military source said.
The state news agency SANA said on Wednesday buses had entered Douma for the third consecutive day to evacuate more rebel fighters and their families to the northern Syrian city of Jarablus, near the border with Turkey.
Under the deal, Syrian state media said Jaish al-Islam would hand over heavy and medium-sized weapons and acknowledge the restoration of the Damascus government's control of Douma.
The towns are located in a section of the Turkish-Syrian frontier where Turkey has carved out a buffer zone controlled on the ground by its military and allied fighters from Free Syrian Army rebel groups that are hostile to Assad.
The Syrian government and the Russian military backing it have demanded that the Army of Islam rebel group leave the area for northern Syria, following a devastating five-week government offensive in eastern Ghouta.
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.
From the start of the humanitarian pause's introduction in eastern Ghouta, 2,269 militants and their families left Douma, the largest urban centre in the eastern suburbs of Damascus, the ministry said.
Russian Federation has been a key backer of Syrian President Bashar Assad, ultimately helping to turn the tide of the devastating civil war in his favor.
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The most powerful Syrian rebel faction on the fringes of Damascus began abandoning its stronghold in the once rebel-held enclave of eastern Ghouta on Monday.
There was no immediate comment from the Army of Islam. He said "humanitarian cases" would be allowed to evacuate on Monday.
Syria and its close ally Russian Federation, which provides military support to Assad's forces, deny using chemical weapons and blame insurgents.
Assad, who has military support from Iran and Russian Federation, now controls the bulk of Syria, though it may be hard for him to recover much more territory without risking a collision with other foreign powers that have forces inside the country.
Turkey, with support from rebels, is running its own military operations against a US -backed Kurdish militia in northern Syria, which controls territory along the frontier.
A local council for Douma would be formed with the approval of the central government, said the government-linked Central Military Media outlet.
"They will all have to agree to the settlement in the end", the source said.