Syrian troops and rebels were locked in fierce clashes on Wednesday night outside the Damascus district of Qabun as the army tried to storm the area, the Syrian Observatory for Human Rights said.
At least two rebel fighters have been killed, with others wounded, the Britain-based group said.
"The district has come under continuous, heavy shelling over the last few hours, killing at least two civilians and wounding others," the Observatory said.
The northeastern neighbourhood of the capital has been a battleground for months, with the military regularly targeting it with shells and air raids.
Meanwhile, near the capital, fighters from Lebanon's Shiite group Hezbollah joined troops in a push to cut off rebel supply lines.
And main opposition National Coalition said it feared a "massacre" was imminent in southern Damascus, as Assad loyalists amassed around rebel areas there.
"Army troops and Hezbollah members fought rebels near the Khomeini hospital in Zayabiyeh village," southeast of Damascus, said the Syrian Observatory for Human Rights.
"Hezbollah fighters, who have a strong presence at Sayyida Zeinab (in southeastern Damascus), are trying to seize control of villages near Zayabiyeh and Babila."
The army shelled both Zayabiyeh and Babila, the group said.
Hezbollah's Al-Manar television reported that the army was advancing towards Zayabiyeh, just south of the confessionally mixed district of Sayyida Zeinab, named after an important Shiite Muslim shrine.
The Lebanese Shiite movement has been fighting alongside the army for months in the district, which lies in an area that rebels from southern Damascus have used as their main rear base.
Signup to our newsletter and follow us on Facebook and Twitter!
Activists say the regime is trying to crush the rebellion on the outskirts of Damascus in order to cut off supply lines to rebel pockets inside the capital.
"There is a fierce campaign against the (rebels) south of the capital... The humanitarian situation is very critical," said Damascus-based activist Matar Ismail.
Ismail said Hezbollah and the Abu al-Fadl Abbas Brigade -- a mostly Syrian Shiite force that has attracted Shiite fighters from elsewhere in the region -- were playing a key role in the fight.
Hezbollah was also credited with an important role in the army's recapture of the rebel stronghold of Qusayr in central Homs province earlier this month.
Meanhwhile, the Coalition warned that Assad loyalists are "staging military operations on 10 axes" in Damascus province, as they try to advance on the south of the capital.
It said rebel-held areas are "under blockade. Food and medicines are not being allowed in."
"Now, regime troops and militiamen backed by Hezbollah and the Abu al-Fadl Abbas Brigade are deploying en masse, with dozens of military vehicles and tanks, rocket launchers and heavy machineguns," the group said.
Some 120,000 people living in strife-torn southern Damascus "are trapped in... fear that (regime) forces may commit a new massacre" there, saying there may be "no way out" for residents.
Elsewhere, fierce battles broke out between rebels and troops in Idlib, in northwestern Syria, the Observatory said.
Opposition forces captured an army post on the road linking the coastal province of Latakia to Ariha in Idlib province, and two tanks were destroyed.
In regime stronghold Latakia, an explosion at an ammunition depot wounded at least 13 soldiers, said the Observatory.
State television said the blast was the result of a technical failure, and that only six had suffered light wounds.