Rebels planned to push into the city centre from their strongholds on the outskirts and fighting has been fierce. The army sent reinforcements after a week of rebel advances, including the capture of two military bases near the capital.
Activists said the heavy rocket attacks yesterday killed at least ten in Deir al Asafir, eight miles east of Damascus, and video footage from the town showed at least five bodies, one a young boy and one an elderly man. Other bodies were wrapped in sheets.
In the central city of Homs, a car bomb killed at least 15 people and wounded 24 yesterday, Syria's state news agency SANA said.
It said the blast in the city's Hamra district also damaged many nearby residential buildings.
There has been a rise in the number of car bombs around Syria. The British-based Syrian Observatory for Human Rights, which has a network of activists across the country, reported four blasts on Saturday.