Mortar shells slammed into several areas of the Syrian capital on Saturday, with one hitting near the Russian embassy without causing injuries, a monitoring group said.
The Syrian Observatory for Human Rights also said regime 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 Observatory reported mortar fire near the Ummayad area and the Russian embassy in the upscale Mazraa neighbourhood of Damascus, with no casualties reported.
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 round 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 escalation came as government troops stepped up a campaign against rebels on the outskirts of Damascus, particularly Eastern Ghouta which has been under regime siege for months.
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The Observatory said rebels and regime troops were fighting in the town of Mleiha in the Eastern Ghouta area.
On Friday, regime 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.
In Idlib, the Observatory reported fighting between regime and rebel forces in the area around Babuleen, which opposition forces captured on Friday.
Their advance has allowed rebel forces to tighten a siege of the Wadi Deif army base, one of the regime's last significant posts in Idlib.
In northern Aleppo city, the Observatory reported regime air raids with explosives-packed "barrel bombs," a day after 18 people were killed in air raids on the east of the city.