Qatari Prime Minister and Foreign Minister Hamad bin Jassim Al Thani urged Assad to step down. With the rebels at the president's doorstep in Damascus, he said, Assad knows the regime will fall.
"But how much killing and destruction does he want before this inevitable outcome?" Hamad said after an Arab League meeting in the Qatari capital, Doha.
In Lebanon, fighting between pro-and anti-Assad gunmen flared as bodies of three Lebanese, who were killed after crossing into Syria to fight in the civil war were brought back home for burial, the state-run National News Agency said.
Four people were killed and 12 were wounded in the gunfights, the agency said. Two Lebanese soldiers were also injured, the Lebanese Armed Forces command said.
Syria civil war has often spilled into neighboring countries including Turkey, Lebanon and Israel, raising concerns of a wider war in the volatile region.
Lebanon, which Syria dominated for decades, is particularly vulnerable to getting sucked into the crisis. The two countries share a porous border and a complex web of political and sectarian ties.
Syria's opposition is dominated by members of the Sunni Muslim minority. Assad's regime is predominantly Alawite, an offshoot of Shiite Islam.
Tripoli has been the scene of frequent sectarian clashes between the Alawite and Sunni Muslim communities. Last week, the Lebanese army sent additional troops to Tripoli to try to prevent clashes that broke out over reports that 17 Lebanese men were killed after entering Syria to fight alongside the rebels.
In Syria, fighting between opposition fighters and regime troops was concentrated in northern Idlib province, in the Damascus suburbs and in Aleppo, Syria's largest city, according to the Britain-based opposition activist group Syrian Observatory for Human Rights. At least 45 people were killed in fighting Sunday, said the group, which relies on reports from activists on the ground.
Syria's state-run SANA news agency said four people were killed when a rocket slammed into the Armenian quarter of the city of Homs. SANA said "terrorists" were behind the attack that also injured several others. Damascus refers to rebels as terrorists and mercenaries of Western and Gulf countries.
The Observatory also said rebels have made significant advances in the battle over a sprawling military base west of Aleppo after heavy clashes with regime troops Sunday.
Associated Press writers Jamal Halaby in Amman, Jordan, Lynn Berry in Moscow, John Heilprin in Geneva, Switzerland, Matthew Lee in Washington, and Abdullah Rebhy, in Doha, Qatar, contributed to this report.