BEIRUT, Jan 13 (Mariam Karouny/Reuters) - Lebanese leaders agreed on Thursday to start talks next week on rebuilding a government after Hezbollah walked out of Prime Minister Saad al-Hariri's coalition, testing political faultlines across the Middle East.

Monday's first meeting will launch a process. But few think a new cabinet likely until compromise is found in the dispute over the possible indictment of Hezbollah figures by a UN tribunal probing the 2005 assassination of Hariri's father.

Deep divisions among Lebanese parties and their powerful regional backers reflect violent religious, ethnic and political rivalries running through the Middle East and beyond, giving leaders from Washington to Tehran a role in Beirut's crisis.

Shi'ite group Hezbollah, which is supported by Iran and Syria, expects the tribunal to accuse its members over the assassination of Rafik al-Hariri. It has denied involvement and called for Lebanon to withdraw all support for the tribunal.

Saudi-backed Saad al-Hariri has rejected those demands, and US officials have said the tribunal's work must continue.

Among U.S. concerns is the risk of a resumption in the war between Hezbollah and Israel which rocked the region in 2006.

The coalition government collapsed on Wednesday, as Hariri met US President Barack Obama. Eleven ministers resigned.

The consultations will start on Monday at noon, the speaker of parliament, Nabih Berri, told reporters after he met President Michel Suleiman. The talks are scheduled for two days.

Both sides are awaiting the indictment. There will be no government before it, said a politician, speaking anonymously.

Hezbollah and its allies blamed the United States for obstructing Saudi and Syrian attempts to find a solution.

Officials have declined to say whether Hariri, whose coalition won a 2009 parliamentary election, will be asked to form a new government, or if someone else would be nominated.

FRENCH, TURKISH MEETINGS

Hariri, who governs for now as caretaker, was to meet French President Nicolas Sarkozy in Paris later before flying to Turkey for a meeting on Friday with Prime Minister Tayyip Erdogan.

Boutros Harb, a parliamentarian close to Hariri, said: I do not see a government in the country without Saad al-Hariri.

The resignations followed the failure of regional powers Saudi Arabia and Syria to forge a deal to reduce tension over the tribunal, which is is expected to send draft indictments to a pre-trial judge this month

Analysts played down the prospect of open armed conflict between Hezbollah and Hariri, a Sunni Muslim who is supported by Saudi Arabia and the United States.

But street protests, skirmishes or even a return to the bombings and political killings that followed the 2005 attack could not be ruled out, analysts said.

The Saudi-Syrian proposals were never spelt out by either country. According to a politician close to Hariri, they would have included a Hezbollah pledge not to resort to violence if its members were indicted, while Hariri would ensure that any indictment was not exploited to Hezbollah's political detriment.

Finance Minister Raya al-Hassan said: We are stumbling in a difficult political situation now.

I hope this phase does not last long... because the economy will go back if it does and in this case we will all be harmed.

Hezbollah, the only armed group not to disband after Lebanon's 1975-90 civil war, is now the most powerful military force in Lebanon, stronger even than the army.

It portrays itself as spearheading Islamic resistance to Israel, not as a sectarian group. That image would be badly damaged if it were proven to have had a role in the huge truck bombing that killed the elder Hariri and 22 other people.

A stalemate over the tribunal had crippled the younger Hariri's government for the last year. The cabinet had met, briefly, just once in the last two months and the government could not secure parliamentary approval for the 2010 budget.