On the frontier with Turkey, too, rebels were said to have taken control of two posts, at Bab al-Hawa and Jarablus.
Video from the Bab al-Hawa crossing in Idlib province soon emerged of rebels defacing a portrait of President Assad, but they later reportedly withdrew from the position.
The BBC's Jim Muir in neighbouring Lebanon says the regime's grip on outlying areas may be slipping, which is hardly surprising given the fighting in Damascus.
State TV has been reporting on violence across the capital, showing footage of troops in the Midan area where it said 20 terrorists had been killed.
Analysts point out that the regime shows no signs of collapsing, and the military is still heavily armed, loyal and able to defend key institutions.
Violence broke out in the capital on Sunday, and two days later the rebels declared an all-out assault, calling it "Damascus volcano".
The explosion on Wednesday that killed three top security officials led to a mobilisation of government troops in an attempt to drive the rebels out of the city.
The president's brother-in-law, the defence minister and head of the government's crisis team were killed by a bomb as they attended a meeting at the national security headquarters.
The first images of President Assad since the attack have appeared, largely ending rumours he might have been hurt.
The footage appeared to show Gen Fahd Jassim al-Furayj, chief of staff of the armed forces, being sworn into his new post as defence minister.
Tanks and armoured vehicles were reported to have moved into Qaboun on Thursday, close to the centre of Damascus.
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