Clashes in the Yarmuk refugee camp pitted pro-regime Popular Front for the Liberation of Palestine-General Command (PFLP-GC) against rebels fighting President Bashar al-Assad's forces, the Syrian Observatory for Human Rights said.
On Sunday unprecedented air strikes on the camp in southern Damascus killed eight civilians, the Observatory said.
But on Monday the pro-regime daily Al-Watan said street battles between the PFLP-GC and rebels had "forced the army to intervene with warplane attacks on the positions of the gunmen."
Residents and the Britain-based Observatory said people in the camp were fleeing en masse on Monday morning for other parts of Damascus, while others scrambled to find safety in safer parts of Yarmuk.
East of the capital, warplanes attacked the Eastern Ghuta region, while smoke was seen rising from nearby Zamalka, which was also raided by jets, the Observatory said.
Military reinforcements were seen travelling from Mazzeh military airport west of Damascus to Daraya farther south, where two rebels were reportedly killed trying to hold back a new assault amid shelling attacks.
"It is a tragic situation today in Daraya. The shelling from Mazzeh airport has not stopped since the morning, and there are fierce clashes on all fronts," local activist Abu Kinan told AFP via Skype, adding that six tanks rolled into the central area of Shameyat.
"We are worried the army will keep bringing reinforcements and abuse the people when they enter," said Abu Kinan.
Around 8,000 residents were trapped in Daraya and "cannot escape because there are snipers at all of the exits," he added.
Video footage showed the Abu Suleiman mosque being pounded by shelling, as billowing clouds of smoke rose to the sky, in what Daraya activists said was the second such attack on the place of worship.
The video could not be immediately verified.
The scene of the bloodiest massacre in the 21-month conflict, Daraya has been under siege by the army for a month and suffered ongoing shelling by troops trying to seize full control.
In the central province of Hama, heavy fighting erupted in Halfaya as rebels attacked army checkpoints and troops shelled the town, where 23 people, mostly civilians, died in clashes and bombardments on Sunday, the Observatory said.
In the eastern province of Deir Ezzor, warplanes raided several towns as insurgents laid siege to the military airbase of the provincial capital.
Fierce clashes also rocked the Handara area in the northern province of Aleppo on Monday, a day after rebels scored a victory taking control of a major infantry academy nearby.
The Observatory, which relies on a network of activists and medics on the ground in compiling its tolls, said 42 people were killed nationwide on Monday, among them seven civilians, a day after 160 died.