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Activists said the Syrian army had attacked southern districts of Damascus with shelling and rocket fire all day to try to stop the rebels seizing the base, in some of the heaviest bombardment of the capital.
"Multiple rocket launchers are just making huge, random destruction," said Rami al-Sayyed of the Syrian Media Centre, an opposition organisation monitoring the crackdown by President Bashar al-Assad's forces.
The Islamist rebel groups Ansar al-Islam and Jund Allah Brigades said in a statement that they had taken the Air Defence Battalion base near Hajar al-Aswad after four days of fighting.
The district had been home to thousands of refugees from the Israeli-occupied Golan Heights. These were at the forefront of the movement against Assad's autocratic rule at the beginning of a revolt that has now turned into a civil war, in which activists say 38,000 people have been killed.
Activists said all the residents had fled under the bombardment.
Video footage showed rebels walking through the site, past destroyed anti-aircraft guns, and one commander saying on a walkie-talkie: "We have completely seized the compound."
Louay al-Dimashki, an opposition activist who said he had documented the fall of the base on video, said the rebels had targeted the compound with mortars then attacked in small groups, killing 14 loyalist troops and taking 35 prisoner.
"The fighters are taking whatever ammunition and weapons they can. They cannot hold on to the base because the regime will hit them from the air," Dimashki said by phone.
Independent verification of the reports was not possible because Syria severely restricts the access of foreign media.
Rebels have captured several army positions in outlying regions in the last week, including a Special Forces base near the northern city of Aleppo and a small military airport in the east, on the border with Iraq.
Inside Damascus, a roadside bomb hit a minibus along a route used by security forces and pro-government media, activists said. The opposition Syrian Observatory for Human Rights said three people had been killed and at least 10 wounded.
Under pressure from foreign states keen to promote a viable and responsible alternative to Assad, Syria's fractious opposition formed a broader coalition group last week, led by moderate Sunni Muslim preacher Mouaz Alkhatib.
The Syrian National Coalition was promptly recognised by France as the sole legitimate representative of the Syrian people.
EU foreign ministers said on Monday they considered the group to be "legitimate representatives" of the Syrian people, stopping just short of the full recognition offered by France.
A group of Islamist fighters in Syria's Aleppo province, many of whom are well-known members of powerful rebel units in the area, said on Monday they rejected the umbrella group and planned to establish an Islamic state in Syria.
Members of Islamist groups listed in a YouTube video as supporters of the plan told Reuters they had nothing to do with the announcement, though they acknowledged that some members of their groups had appeared in the video.
This could suggest cracks in Islamist rebel ranks over how to respond to growing efforts to unify rebel groups and potentially sideline more radical Islamist elements.
The expanding conflict has threatened to suck in Syria's neighbours, especially Turkey in the north.
Syrian mortar rounds have fallen in Turkey, Lebanon and Israel as rebels hug the borders looking for safety, and Turkey's army is stationing soldiers in recently dug trenches along the border.