Opposition fighters reportedly fired at the Syrian presidential palace, but missed, and shelled the Mazzeh military airport and intelligence headquarters in Damascus, Al Arabiya TV reported on Wednesday.
The attacks were an indication of the violence moving increasingly from the suburbs into districts of the Syrian capital.
A car bomb exploded overnight in the southern Qadam neighborhood, causing at least one death, said the Syrian Observatory for Human Rights, a Britain-based watchdog that relies on a network of activists and medics on the ground.
Wednesday's attempted mortar strike on Assad's palace drew comparisons with a bomb attack in a highly guarded district of Damascus in July that killed four of the president's top lieutenants.
In the Mazzeh district, home to many embassies and offices of the security services, three civilians were killed and 12 wounded from mortar fire, it said.
Opposition fighters, meanwhile, clashed with pro-regime Palestinian forces in the southern Hajar al-Aswad district and the nearby Palestinian refugee camp of Yarmuk, AFP reported, which has become a new focal point of violence.
10 members of the Popular Front for the Liberation of Palestine-General Command (PFLP-GC), a faction loyal to President Bashar al-Assad, were killed by rebel fighters, Reuters reported.
Home to some 148,000 residents, the camp has been the scene of fierce fighting between the rebels and the PFLP-GC.
Wednesday’s violence followed bomb attacks in the suburbs of Damascus on Tuesday, including three explosions in the western Qudsaya area, that killed 19 people and wounded more than 50, according to the Observatory.
Elsewhere in the country, regime air power kept up strikes over northern Aleppo and the surrounding region on Wednesday as rebels continued their months-long battle for control of the commercial hub.
The violence on Tuesday left 150 dead, including 79 civilians, 48 soldiers and 23 rebels, said the Observatory, which says 36,000 people have died since the outbreak of the revolt against Assad’s regime in March 2011.
Cameron visits Syrian refugee camp
British Prime Minister David Cameron on Wednesday toured a desert refugee camp for Syrians in northern Jordan, walking down a dusty road between the tents before visiting a U.N.-run school.
“Right here in Jordan I am hearing appalling stories about what has happened inside Syria so one of the first things I want to talk to Barack about is how we must do more to try and solve this crisis,” he said in an official statement released in London.
His comments came in a message of congratulations to U.S. President Barack Obama on his re-election.
Dressed casually in black trousers, a grey shirt and a sporting a Remembrance poppy, Cameron took time to speak to some of the more than 36,000 Syrians housed in tents and caravans in the Zaatari refugee camp near the Syria border.
The British premier arrived in Jordan on Tuesday night on the last leg of Middle East visit that also took him to the United Arab Emirates and to Saudi Arabia.
On arriving at the camp early morning, Cameron headed to offices of the United Nations, which runs the camp, before touring the facility.
Crowds of excited kids played football but did not seem to know who the visitor was.
“Is he the king?” one of them asked.
Inside the school, a group of children sang to Cameron in Arabic. The prime minister left the camp after visiting the school and was later to hold talks with Jordan’s King Abdullah.
The visit to the camp comes after Cameron told Al Arabiya on Tuesday he would support granting Assad a safe passage out of Syria to end the nation’s bloodshed.
Jordan says it is hosting more than 200,000 Syrian refugees, who have fled violence ravaging their homeland since a popular uprising erupted more than 19 months ago.