BEIRUT, May 25 (Reuters) - The Syrian army said it had retaken a swathe of territory from Islamic State in southern Syria on Thursday in a rapid advance near areas held by U.S.-backed Syrian rebels at the border with Jordan and Iraq.

The Syrian government said earlier in May that it was a priority to recapture the sparsely populated region known as the Badia where U.S.-backed Syrian rebels seized a vast expanse of territory from Islamic State in March.

Tensions flared in the southern region last week when the U.S.-led coalition mounted an air strike against pro-government forces that U.S. officials said posed a threat to U.S. and U.S.-backed Syrian fighters in the area. Washington described the forces as Iranian-directed.

The Syrian army on Thursday declared the capture of areas to the south of Palmyra and to the east of Qaryatayn in southeastern Homs province. State TV showed footage of military vehicles including tanks driving through a desert landscape.

A military source told state news agency SANA that dozens of Islamic State fighters had been killed in the operation that resulted in the destruction of large quantities of weapons and ammunition and followed gains in the same area 48 hours earlier.

The advance by the U.S.-backed rebels into the Badia in March was assisted by Islamic State's retreat to other parts of Syria, where the group is facing separate offensives by U.S.-backed forces and the Russian-backed Syrian army and its allies.

The coalition has been training the rebels to fight Islamic State at a garrison in al-Tanf, a strategically vital location at the intersection of the Jordanian, Iraqi and Syrian borders.

An official with one of the Free Syrian Army (FSA) rebel groups operating in southern Syria told Reuters that government forces appeared to be trying to preempt any rebel move towards Deir al-Zor, another priority target for the government.

"The advances help the regime to widen the security belt around the Damascus and also will pave the way for a (government) push towards Deir al-Zor before the FSA groups by capturing territory in the northeast of the Badia that makes it difficult for (FSA groups) to advance in that direction," Said Seif, an official in the Shahid Ahmad Abdo FSA group, said.

Deir al-Zor province is held mostly by Islamic State. The government still has a foothold in the city of Deir al-Zor, and controls a nearby air base.

(Reporting by Tom Perry in Beirut and Suleiman al-Khalidi in Amman; Writing by Tom Perry; Editing by Tom Heneghan) ((thomas.perry@thomsonreuters.com; Reuters Messaging: thomas.perry.reuters.com@reuters.net))