The ruling coalition's refusal to yield to the opposition's demand for veto power in cabinet triggered the resignation of all Shi'ite ministers in November 2006, crippling a political system build around the delicate sectarian balance.
Power-sharing in a new government and the basis of an election law are the core issues on the agenda. The ruling coalition also raised the matter of Hezbollah's weapons after the anti-Israel group turned its guns against political rivals.
Bush said Hezbollah had abused its position. "It is clear that Hezbollah, which has been funded by Iran, can no longer justify its position as a defender against Israel when it turns on its own people," he said.
Delegates said politicians from the Western-backed camp and Hezbollah had got into a heated debate over the prickliest issue and the one that led to the recent clashes -- Hezbollah's arms.
Sheikh Hamad intervened to end that debate, which he said should be postponed until after a deal is clinched to end the political stalemate and allow for the election of a president.
Hezbollah says its arms are meant to protect Lebanon against its Israeli foe. Opponents, trounced in the fighting, argue they undermine the sovereignty of the state.
"There is a real will on all sides; everyone lost with what happened. The winner (Hezbollah) is the bigger loser, because it opened up the important issue of the use of weapons," said Michel Pharaon, a minister in the U.S.-backed government.
"It is imperative that there be discussions on the sovereignty of the state ..."
There has been no deadline set for the talks but some politicians said a deal could be reached within a few days.
"The issue is not simple," government minister Ahmad Fatfat said. "Everyone will work day and night to reach a solution."
Syria, which backs the opposition and is an ally of Iran, said it supported the Qatari-led Arab League initiative.
The anti-Damascus factions have long accused the opposition of seeking to restore Syrian domination over Lebanon, which ended in 2005 when Syria withdrew its troops in the face of international pressure and Lebanese protests.
Saudi Arabia, a strong backer of the ruling coalition, also stated its support for the deal.
A deal would lead to the election of army commander General Michel Suleiman as president. Both sides have accepted his nomination for a post reserved for a Maronite Christian in Lebanon's sectarian power-sharing system.
