Syrian troops and rebels battled in several southern and eastern districts of Damascus on Thursday, the Syrian Observatory for Human Rights said, adding the army used heavy artillery to target some insurgent positions.
Clashes that began a day earlier in the north-eastern Qabun neighbourhood were continuing, as army troops sought to storm the district, firing mortar shells and heavy artillery, the Observatory said.
Several homes in the area caught fire as a result of the bombardment, the group said.
The northern Barzeh district and eastern Jubar neighbourhood, both home to pockets of rebel fighters, were also under fire.
In the south of the capital, the contested neighbourhoods of Al-Hajar al-Aswad and Qadam were the scene of ongoing clashes, with shelling forcing the closure of the road leading to the Palestinian Yarmuk refugee camp.
A woman and a child were killed by an army sniper in the area, according to the Observatory, which relies on a network of activists, doctors and lawyers on the ground.
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Rebel have established rear bases in parts of the southern and eastern districts of the capital, prompting the Syrian military to launch raids in a bid to uproot them.
Earlier this week, a rebel attack in Qadam killed 11 Syrian soldiers.
In southern and eastern suburbs of the city, rebels were also battling troops backed by members of the Shiite Lebanese group Hezbollah, the Observatory said.
Government troops are pushing in particular to retake the village of Zayabiya and Babila, south of the capital, mixed Sunni-Shiite villages near the Sayyida Zeinab shrine, a Shiite pilgrimage site.
The Observatory said Hezbollah fighters were present in force around Sayyida Zeinab, from which they were launching attacks on the two villages.
The group, a strong ally of the Syrian regime of President Bashar al-Assad, has played a key role in at least one battle in the conflict, helping the army win back control of the town of Qusayr in central Homs province earlier this month.
At least 133 people were killed in violence throughout Syria on Wednesday, according to the Observatory.