Mortar shells have hit several areas of the Syrian capital, with one falling near the Russian embassy, a monitoring group said.
The Syrian Observatory for Human Rights also said government troops battled rebels in eastern Ghouta near the capital, while opposition forces tightened their siege of a military base in Idlib province of northwest Syria.
The Britain-based group also reported mortar fire in the southern Shughur district and nearby Fahama, where a number of security buildings are located.
Syria's state news agency SANA reported 17 mortar bomb attacks across the city, causing damage to a hospital as well as several homes and cars.
Mortar shell attacks on the capital on Friday injured 22 people, it said, without giving a toll for Saturday.
The violence came as government troops stepped up a campaign against rebels on the outskirts of Damascus, particularly Eastern Ghouta which has been under government forces siege for months.
The Observatory said rebels and government troops were fighting in the town of Mleiha in the Eastern Ghouta area.
On Friday, government warplanes carried out air strikes as soldiers tried to storm the town.
The fighting left 17 rebels dead on Friday, a day after 22 opposition fighters were killed in and around Mleiha, according to the Observatory.
In nearby Jaramana, SANA reported "terrorist mortar shell attacks" injured 13 people on Saturday.
The army siege of Eastern Ghouta has led to food and medical shortages, which the Observatory said had caused the death of a child on Friday.