"The district of Qaboon in (northeastern) Damascus is being intensely shelled by regime forces," the Syrian Observatory for Human Rights reported.
Rebels were resisting the onslaught, battling troops loyal to President Bashar al-Assad on the edges of Qaboon as the army tried to storm the neighbourhood, it said.
Overnight mortar fire targeting Qaboon killed three children from one family, the Britain-based group said.
Nearby, clashes raged between rebels, troops and pro-Assad militiamen in the Barzeh neighbourhood of the capital, said the watchdog.
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Battles also raged on the edges of Al-Hajar al-Aswad in southern Damascus and Jubar in the east, said the Observatory. Troops meanwhile pounded the Qadam district, parts of which are rebel-held.
Over the past fortnight, the army has dramatically boosted efforts to crush the anti-Assad insurgency in and around Damascus.
The opposition and activists have warned of critical humanitarian conditions in some areas.
Also today, the military pushed on with its bid to end the insurgency in and around Homs in central Syria, said the Observatory.
Referred to by activists as "the capital of the revolution", Homs has suffered massive damage during Syria's 27-month conflict.