Shelling killed at least 13 people on Sunday in the Damascus district of Qaboon, where fierce fighting between the army and rebels has trapped hundreds of families, a monitor said.
The Syrian Observatory for Human Rights also reported a car bomb detonated outside a police station in Damascus province, killing at least three people and wounding dozens of others.
"The toll from shelling on Qaboon rose to 13 people," the Observatory said, adding three civilians and seven rebels were among the dead, and that three bodies had not yet been identified.
The deaths came after the Observatory warned that hundreds of families were trapped in the northeastern district by fierce fighting between troops and rebel fighters.
"There is a siege because regime snipers are posted on the outskirts of Qaboon and this makes any attempt to leave difficult," said the group. "The area has also been bombed by the army."
Regime troops have been trying for months to dislodge rebels from rear-bases they have established in parts of the outskirts of Damascus.
Footage filmed by activists in Qaboon showed smoke rising from the area as the sound of non-stop artillery and mortar fire rings out.
The Observatory said residents of the area were facing a "stifling" siege.
"There's a major shortage of food and some families have nothing to feed their children with," it said.
The Observatory also reported that dozens of people detained in an underground makeshift prison near a mosque in Qaboon escaped when regime forces guarding the site left to join the fighting.
Overnight, the opposition National Coalition had urged the international community to act to free "200 people" they say are being held in the mosque.
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Rebels fighting to overthrow President Bashar al-Assad's government control several neighbourhoods on the outskirts of Damascus from which they are able to shell areas in the city centre, which is still in regime control.
Forces loyal to Assad have for months been trying to uproot those rear-bases, including in Qaboon and Barzeh, in northern Damascus.
Meanwhile a car bomb exploded outside a police station in the Damascus province town of Deir al-Attiya killing at least three men and wounding dozens of people, the Observatory said.
Observatory chief Rami Abdel Rahman told AFP details were still scarce but reports indicated that the death toll could rise and that policemen could be among the casualties.
The bombing caused heavy damage to the police station.
The Observatory reported fighting throughout Syria, including in the northwestern province of Idlib, where a man and his three children were killed in a helicopter gunship raid.
In the same province, a rocket attack killed five people, including two women, at Jabal Zawiya, and an air strike killed three people in the town of Kafr Nabl.
The Observatory also reported that the Red Crescent delivered 5,000 food rations to Aleppo's central prison, which has been under siege by rebel forces for three months.
"Rebels allowed them to bring in rations for the Muslim month of Ramadan," it said.
At least 120 prisoners died in the facility in May alone as a result of shelling and food and medical shortages, said the Observatory.
Rebel forces have been seeking to capture the prison and free around 4,000 people inside, who include political prisoners as well as common criminals.