The diplomatic maneuvering comes as Syria has been wracked by violence that began when demonstrators inspired by Arab Spring popular uprisings in Egypt, Tunisia and Libya took to the streets to demand reforms.
A brutal crackdown on the protests by government forces quickly spiraled into an armed conflict, with the rebel Free Syrian Army now serving as a fighting force countering al-Assad's military.
Despite enormous international pressure, al-Assad has defied calls to step down. He has blamed violence on "terrorists" bent on destabilizing his government.
On Saturday, the government said its forces had attacked a number of rebel operations in the eastern Syrian city of Deir Ezzor, according to the state-run Syrian Arab News Agency.
The news agency reported that during the operations, government forces killed Ismail Mohammad al-Alloush, the leader of the rebel al-Furqan Brigade, and rebel commander Mohammad Sabbar Khalifa.
The opposition, meanwhile, accused government forces of shelling the southern town of Busr al-Harir in an effort to retake it from rebels.
The Free Syrian Army took the town, which lies along the Daraa-Damascus highway, on Friday, according to the LCC. Al-Assad's forces surrounded the town Saturday and fired rockets and mortar rounds, the opposition group said.