The Syrian Observatory for Human Rights said the fighting erupted in the village of Basr al-Harir before dawn on Sunday.
Heavy machine-gun exchanges have also been reported in the town of Dael, but there are no immediate reports of casualties.
On Friday, an explosion that targeted a police bus in central Damascus also killed more than 20 people and injured over 60 others.
Syria has been experiencing unrest since mid-March. The Arab League observers prepare to issue their first findings on the unrest in Syria at a meeting in Cairo later on Sunday.
The United Nations said in mid-December that more than 5,000 people have been killed in the turmoil.
Damascus says over 2,000 of those killed were members of its security forces.
The West and the Syrian opposition accuse the government of killing protesters. Damascus blames ”outlaws, saboteurs and armed terrorist groups” for the unrest, insisting that it is being orchestrated from abroad.