The group said in a statement it had attacked the Tishrin power station, 30 miles northeast of the capital.
The Syrian military source acknowledged the group had staged assaults, but said all those who took part had been killed.
Syrian and allied forces backed by Russian airstrikes have forced ISIS terrorists out of the town of al-Qaryatain, which lies between Damascus and the ancient city of Palymrya, itself recaptured by the government last week.
ISIS has also been losing ground to Kurdish forces in northern Syria, and in recent days to Turkish-backed rebel groups fighting a separate battle against the group north of Aleppo.
Also ISIS attackers, using five bomb-laden cars, struck military positions near the Dumeir military airport 25 miles northeast of Damascus, the London based Syrian Observatory for Human Rights reported.
Government forces responded with shelling and airstrikes around the Dumeir area, which is held by a rebel group sympathetic to ISIS, the Observatory said, Daily Mail reported.
Syrian Army strikes have killed at least 15 ISIS terrorists, as well as the drivers of its five bomb-laden cars, died in the clashes.
The Syrian military source said 13 of the group's fighters had been killed in clashes in the area around Dumeir.
Also fighting with ISIS militants raged in northern Syria on Thursday. Syrian opposition rebels have advanced on strongholds of the terror group, including the ISIS-held town of al-Rai in northern Aleppo along the Turkey border.
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