The rebels issued a video documenting the structure which seems to be damaged at the roof, though whether the damage is the result of bombs cannot be determined by the video.
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As can be seen in signs, featured on the damaged structure, attributing the synagogue to Prophet Elijah, the synagogue is traditionally considered to be marking the spot where Elijah anointed Elisha as a prophet.
The damaged Damascus synagogue
Meanwhile, the Britain-based Syrian Observatory for Human Rights activist group said clashes were still raging around Aleppo's landmark 12th century Umayyad Mosque in the walled Old City, which is a UNESCO World Heritage Site.
The mosque was heavily damaged last year just weeks after a fire gutted the city's famed medieval market.
There were conflicting reports about whether the rebels had managed to force regime troops out of the mosque and take full control of the holy site.
Mohammed al-Khatib of the Aleppo Media Center activist group said the mosque was in rebel hands, although clashes were still raging.
"The regime forces left lots of ammunition in it (the mosque), with guns and rocket-propelled grenades," he said via Skype.
Observatory director Rami Abdul-Rahman said rebels have been in control of at least half of the mosque complex for days, but he could not confirm that they had captured all of it.
Near the capital of Damascus, activists said the bodies of ten men — most of them shot in the head — were found dumped on the side of a road between the suburbs of Adra and Dumair. Such incidents have become a frequent occurrence in the civil war.
AP contributed to this report
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