Rebels also clashed with the army on both sides of the capital's southern boundary, including in the neighborhoods of Tadamon and Yarmouk. Residents of southern neighborhoods said they could hear blasts and see smoke rising from government shelling near the rebel-held suburb of Daraya.
The Britain-based activist group Syrian Observatory for Human Rights reported clashes and shelling east and south of Damascus, saying at least 40 people were killed in and around the city.
The state news agency said the army was pursuing rebels in Jobar and other areas east of the city and had killed an unspecified number of them.
The sounds of the nearby violence terrified residents. Few cars were on the roads and many shops were closed.
In central Damascus, a coffee merchant named Waleed stood in front of his shop, listening to the blasts in the distance.
“Most of my neighbors have shut and gone home, and I'll shut too in a bit,” he said, giving only his first name because of fears for his safety.
“How can these people keep shelling, and how many people have they killed?” he asked “May God punish the oppressor.”
The Observatory also reported two car bomb blasts in the ancient city of Palmyra in central Syria. One targeted the local branch of Syria's military intelligence agency, killing at least 19 security officers and wounding many more. A second and apparently coordinated bomb hit another security office. Eight civilians were wounded in gunfire and explosions following the two attacks, the Observatory said.
An online video purportedly shot in Palmyra showed a huge gray mushroom cloud rising over the city.
All videos appeared genuine and corresponded to other reporting by The Associated Press.
The state news agency confirmed the blasts but said two suicide bombers blew up their cars near a garage, killing and wounded an unspecified number of people.
No one claimed responsibility for the blasts. Some rebel groups have acknowledged carrying out suicide attacks on government targets.
The government blamed the blasts on “terrorists” — its blanket term for the opposition.
Activists also reported fierce clashes near the northern city of Aleppo, where rebels have attacked army convoys heading to a military complex near the town of al-Safireh. At least 12 fighters were killed there, the Observatory said, while a shell attack on the nearby city of al-Bab killed five members of the same family.
More than 60,000 people have been killed since Syria's conflict started in March 2011. Some 700,000 people have fled to neighboring countries and more than 2 million remain displaced inside Syria.