The source said combat operations would accelerate toward the town of al-Sukhna, some 50 km from the administrative frontier of Deir ez-Zor province, where Daesh has redeployed many fighters after losing ground in Syria and Iraq.
"Capturing al-Sukhna means opening the door and path for forces to move to Deir ez-Zor directly," the source told Reuters, adding that the military had captured positions 8 km southwest of the town on Wednesday evening.
Daesh is losing ground fast in Syria to separate campaigns waged by the Syrian government on the one hand, and to Kurdish forces on the other.
Government forces, backed by the Russian air force, have also been advancing against Daesh in Hama province and in southern areas of Raqqa province.
The Syrian forces have been approaching al-Sukhna gradually since capturing the ancient city of Palmyra, some 50 km away, in March.
"It is natural that combat operations escalate in this direction and take on a stronger and faster nature," the source said, adding that Daesh had concentrated forces in al-Sukhna.
Deir ez-Zor province, which borders Iraq to the east, is almost entirely under Daesh control. The Syrian government has held on to a pocket of territory in the provincial capital of Deir ez-Zor city, and at a nearby air base.