There was no immediate comment from the rebels in the eastern Qalamoun pocket of territory northeast of Damascus.
|Smoke rises from Yarmouk Palestinian camp in Damascus.|
The eastern Qalamoun area is 40 km (25 miles) from Damascus and includes several towns an expanse of mountainous territory.
State TV said 3,200 militants and their families were expected to leave the area in preparation for them to be transported to Idlib and Jarablus, a rebel-held territory at the border with Turkey.
The Syrian military and its allies meanwhile pressed the bombardment of a besieged enclave south of Damascus. State TV footage showed clouds of smoke rising from the al-Hajar al-Aswad district, part of an enclave including the Palestinian Yarmouk camp that is held by Islamic State and other jihadist groups.
UNRWA, the UN agency that cares for Palestinian refugees, has said it is deeply concerned about the fate of thousands of civilians including Palestinian refugees in Yarmouk and the surrounding areas.
The conquest of eastern Qalamoun and the enclave south of Damascus will leave just one remaining besieged rebel enclave, north of the city of Homs.
Large parts of Syria at the borders with Jordan, Israel, Turkey and Iraq remain outside Assad's control, however. Anti-Assad rebels hold a chunk of territory in the southwest and the northwest, and Kurdish-led militias, backed by the United States, control an expanse of northern and eastern Syria.