By Rebecca Harrison and Ori Lewis

JERUSALEM, Jan 31 (Reuters) - Ehud Olmert has told allies he will stay on as Israeli prime minister after an official inquiry into the 2006 Lebanon war granted him a reprieve and gave him a boost for U.S.-backed peace talks with the Palestinians.

An official in Olmert's office said on Thursday the prime minister would implement recommendations laid out by the government-appointed Winograd Commission on Israel's 2006 war against Hezbollah guerrillas and would "continue to work".

Political allies said Olmert would not quit, and would soon try to build a broader coalition better placed to pursue divisive talks to forge a deal on Palestinian statehood before U.S. President George W. Bush leaves office in a year.

"I was at his place last night. He said that even had the Winograd Commission been firmer in its criticism, he would not have stepped down," Yosef Lapid, former justice minister and Olmert confidant, told Reuters. "But given the way it turned out -- certainly not. He said this to me."

Olmert won key backing within his own Kadima party. Foreign Minister Tzipi Livni, who called for him to quit over a scathing interim report in April on the war, said the government should "stay and fix" the faults, according to a political source.

The Winograd Commission's final report issued on Wednesday described "serious failings" by political and army leaders during the war, but did not blame Olmert personally and endorsed key and controversial decisions he made.

Olmert's political rivals had been positioning themselves for a resignation that could have triggered an early election. But the report was widely seen by commentators as a reprieve for the man who once described himself as "indestructible".

"The exoneration and the failure" was how Yedioth Ahronoth described the 500-page final report in a banner headline. One columnist said Olmert could "breathe a sigh of relief".

PEACE TALKS

Israel and the Palestinians agreed in November to restart peace talks after a seven year hiatus but Olmert's fractious coalition and his own fragile political standing were seen as an Achilles heel of the peace drive.

Palestinian negotiator Saeb Erekat voiced hope on Thursday the Winograd report would "clear the way for a meaningful peace process that would end the Israeli occupation".

The war battered Olmert's approval ratings. He has also been plagued by graft allegations, which he denies, and lost a rightist coalition ally this month over his peace moves.

But a poll in the Maariv daily showed Olmert's popularity appeared to have rallied, with 42 percent of respondents wanting him to stay on as prime minister, compared to only 17 percent after the interim report was issued in April. A television poll on Wednesday showed 27 percent wanted him to carry on.

Retired Supreme Court justice Eliahu Winograd was scathing about the military. He called the conflict a "missed opportunity" that ended without clear victory over Hezbollah, which pounded northern Israel with rockets.

"A few thousand men resisted, for a few weeks, the strongest army in the Middle East," he said of the Islamist fighters during a news conference to present the report's findings.

Lebanese army commander General Michel Suleiman, a presidential nominee with close links to Hezbollah, told Lebanon's as-Safir newspaper the report proved Israel reaped "destruction, damage and victims without having any excuse".

Some 1,200 Lebanese were killed, 900 of them civilians, while Israel suffered 159 mostly military casualties.

(Additional reporting by Adam Entous and Ori Lewis in Jerusalem, Mohammed Assadi in Ramallah and Yara Bayoumy in Beirut; Writing by Rebecca Harrison; Editing by Diana Abdallah)

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