Among those killed were five civilians, three of them women, who died when mortars slammed into the Yarmuk Palestinian refugee camp in the south of the capital, the Syrian Observatory for Human Rights said.
The watchdog and a Syrian security official had on Wednesday reported the launch by President Bashar al-Assad's forces of a fierce offensive on rebel belts on the outskirts of Damascus, while residents reported the heaviest bombardments in months.
The Observatory reported on Thursday that 21 civilians, 32 rebels and 11 soldiers have been killed since the launch of the offensive, which is focused in the southern and eastern outskirts of the capital.
It said that rebels on Wednesday attacked a security checkpoint between the northeast Qaboon district and Abassid Square near the centre of the capital, sparking fierce fighting.
Pro-regime daily Al-Watan reported on Thursday that "terrorists in Jobar (east) who attacked army checkpoints perished at the gates of Damascus on the perimeter of Abassid Square. They could not advance."
The paper said the army "destroyed the proponents of the 'epic' battle for Damascus," referring to a rebel offensive on the capital.
"The army is determined to crush terrorism around the capital and big cities, and over the past several days it has launched a qualitative operation and killed dozens of terrorists who dreamt of attacking and entering Damascus."
The Britain-based Observatory also reported the arrival Thursday of new military reinforcements at Daraya, an embattled southwestern suburb of Damascus that has been under continuous army bombardment for months.
In the Yarmuk camp, five civilians including three women were killed when mortar rounds fired during fighting in nearby Tadamun district landed among the refugees.
Also on the outskirts of the capital, loyalist troops pounded rebel positions across the east and in the south, the Observatory said, as clashes broke out around a military vehicles depot to the northeast.
These areas of Damascus are among the strongest bastions of the rebellion against the Assad regime, which is battling to suppress a nearly two year revolt that has left over 60,000 dead according to the UN.
The Observatory, which gathers its reports from a large network of activists and medics in civilian and military hospitals on the ground, said that 160 people were killed nationwide on Wednesday: 75 rebels, 46 soldiers and 39 civilians.