The army pushed into the city this month with the help of Russian air power and Iran-backed militias, breaking Daesh siege of an enclave there that had lasted three years.
On Sunday, the Syrian army and allied forces captured al-Jafra district on the western bank of the Euphrates river, the military source said.
“They have no outlet except crossing the Euphrates towards the eastern bank and fleeing towards the desert, or (the towns) al-Bukamal and al-Mayadin,” the source told Reuters.
Moscow and Washington are backing separate offensives in the oil-rich province of Deir al-Zor bordering Iraq. Both have advanced from opposite sides of the Euphrates which bisects the province, Islamic
State’s last major foothold in Syria.
Russian- and U.S.-backed offensives against Daesh have mostly stayed out of each other’s way, with the Euphrates often acting as the dividing line.
But the Pentagon accused Russia this week of bombing U.S.-backed forces on the river’s eastern bank.
Russia’s Defence Ministry rejected the allegations on Sunday. Moscow had warned the United States well in advance of its operational plans and its jets only targeted Daesh militants, it said.