The uprising started in March 2011 as peaceful protests but quickly turned into a civil war after the government's brutal crackdown on dissent. Activists say more than 40,000 people have been killed.
On Sunday, fighter jets screamed over Damascus to bomb two areas in the southern part of the capital.
The Britain-based Syrian Observatory for Human Rights said fighter jets carried out six airstrikes the Hajar Aswad area and the neighboring Yarmouk Palestinian camp, where the rebels have been advancing.
Eight people were killed in the airstrike on Yarmouk, the Observatory said, and dozens were wounded. At least three people were killed in the clashes between rebels and gunmen loyal to Assad that followed the air strike, said Rami Abdul-Rahman, the Observatory's president.
The Observatory relies on reports from activists on the ground.
The Palestinians are divided over the crisis in Syria. When the unrest began in March 2011, the half-million-strong community tried to stay on the sidelines.
A few groups with longstanding ties to the regime are fighting on the government side, including the Popular Front for the Liberation of Palestine-General Command.
An activist video posted online after the attack on Yarmouk shows scattered glass, debris and twisted metal on a narrow street. Gravely injured people are seen lying on the street in pools of blood.
The videos appear consistent with AP's reporting from the area.
In Ramallah, Palestinian officials blasted the Syrian government for the attack.
"We condemn in the strongest terms the crime of Assad's regime in Yarmouk refugee camp, and call on all international parties, including the states that still back this regime, to act immediately and stop these massacres against Syrians and Palestinians in Syria," PLO official Yasser Abed Rabbo told the AP.
Anwar Rajja, a Damascus-based spokesman for the PFLP-GC told the AP that his group is fighting "terrorists," who have come to the camp from the front lines in the suburbs of Damascus. The Syrian regime and state media refer to the rebels as terrorists.
Associated Press writer Maamoun Youssef in Cairo, Mohammed Daraghmeh in Ramallah, West Bank, and Albert Aji in Damascus, Syria, contributed to this report.