He and other activists said the Shiite gunmen were from Lebanon's Hezbollah militant group.
A local Lebanese official in Hermel, near the border, said a group of Hezbollah fighters had entered Syria to protect the Shiite villages. Two of them were killed and 10 were wounded, he said, speaking on condition of anonymity because he was not authorized to discuss Hezbollah matters.
A Hezbollah spokesman declined to comment.
The Britain-based Syrian Observatory for Human Rights said the clashes killed 10 rebels and three Shiite gunmen, noting that many Lebanese live in the Shiite villages.
Most of the area's Shiites support Hezbollah.
Earlier Sunday, Syrian Electricity Minister Imad Khamis told the state news agency, SANA, that electricity has been restored in most parts of the Syrian capital and that power would gradually return to the south. He blamed the blackout on an unspecified fault in high-voltage lines.
The power outage plunged Damascus into darkness late Saturday and affected much of southern Syria, mainly the provinces of Daraa and Sweida along the Jordanian border.
A similar blackout struck the same areas on Jan. 20. The government blamed that outage on a rebel attack, and power was restored to most areas the following day.
Also Sunday, an explosion in traffic circle northwest of downtown Damascus killed one person and wounded another, a security official said, speaking on condition of anonymity because he was not authorized to brief the media.
It was unclear what caused the blast in Abbasid Square, which sits on the western side of the neighborhood of Jobar, where rebels from the suburbs have been trying to push in the capital and clashing with government troops for more than a week.
The U.N. says nearly 70,000 people have been killed in Syria's conflict since the revolt began in March 2011.
In a related development, U.N. High Commissioner for Human Rights Navi Pillay pressed for international action to help stem the bloodshed, but acknowledged that achieving that won't be easy. She alleged that Assad's regime had committed crimes against humanity and should be referred to the International Criminal Court.
Hendawi reported from Cairo. Associated Press writers Albert Aji in Damascus, Syria, Ben Hubbard in Beirut and Geir Moulson in Berlin, Germany, contributed to this report.
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