* Leaders to begin substantive talks

* Chances of success seen 50-50

By Nadim Ladki

DOHA, May 17 (Reuters) - Lebanon's rival leaders hold talks in Qatar on Saturday to try to end a political conflict that has pushed their country to the brink of a new civil war.

"The task ahead of you is a great and difficult one," Qatari Emir Sheikh Hamad bin Khalifa al-Thani told government and opposition leaders at the opening session on Friday night.

On Thursday, Arab mediators reached a deal to end Lebanon's worst internal fighting in nearly two decades and create a framework for the talks hosted by Qatar.

The clashes killed 81 people and exacerbated sectarian tensions between Shi'ites loyal to the Iranian-backed Hezbollah group and Druze and Sunni followers of the U.S.-supported ruling coalition.

"We hope that we will finish what we have started. I'm optimistic," said Arab League Secretary-General Amr Moussa, who together with Qatar's prime minister helped broker the agreement which ended the fighting.

The political standoff has paralysed government for 18 months and left Lebanon without a president since November.

In a sign of the distrust which the talks must overcome, government and opposition leaders waited in separate halls for the brief opening session, which adjourned after Sheikh Hamad's address.

But some leaders did engage in informal discussions during the flight from Beirut, politicians from both sides said.

They said substantive talks would begin in Saturday, when the leaders are scheduled to discuss power sharing in a new government and the basis of an election law.

HEZBOLLAH WEAPONS

Some leaders of the ruling coalition are expected to demand Hezbollah's weapons be the first item on the agenda after the anti-Israel group turned its arms against its political rivals.

"Chances of success and failure are 50-50. It is a very complex crisis and the hurdles are so big that it would require a huge effort to resolve," one politician said.

Washington blames Syria and Iran for Hezbollah's brief seizure of parts of Beirut last week which forced the government to rescind two decisions which had triggered the escalation.

The opposition has demanded more say in a cabinet controlled by factions opposed to Syrian influence in Lebanon.

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 that was ended in 2005 when Syria, under international pressure, withdrew its troops after the killing of former Prime Minister Rafik al-Hariri.

Saudi Arabia, a strong backer of the ruling coalition, also stated its support for the deal. Riyadh said this week that Hezbollah's campaign could affect Iran's ties with Arab states.

Saudi Foreign Minister Prince Saud al-Faisal, speaking in Riyadh, stressed the importance of all parties abiding by commitments not to use violence for political gain.

The ruling coalition's refusal to yield to the opposition's demand for veto power in cabinet triggered the resignation of all its Shi'ite ministers in November 2006. Lebanon was plunged into its worst political crisis since the civil war.

A deal would lead to the election of army commander General Michel Suleiman as president. Both sides have long accepted his nomination for a post reserved for a Maronite Christian in Lebanon's sectarian power-sharing system. (Editing by Philippa Fletcher)

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