By Jeffrey Heller

JERUSALEM, Jan 17 (Reuters) The resignation of Israel's armed forces chief over failure to win last summer's Lebanon war dealt a fresh blow today to Prime Minister Ehud Olmert, already weakened by political scandal.

Israeli media described Lieutenant-General Dan Halutz's decision to quit as an earthquake and speculated whether it might ultimately trigger a domino effect toppling Olmert and Defence Minister Amir Peretz.

The former fighter pilot's resignation was announced hours after Israel's state prosecutor ordered a criminal probe into Olmert's role in the privatisation of Israel's second biggest bank in 2005, when he was finance minister.

''The investigation of Olmert and Halutz's resignation in the wake of the Lebanon war could rock the foundations of the government,'' political analyst Hanan Crystal said on Israel Radio.

Olmert has denied any wrongdoing in the sale of Bank Leumi or in another case, now being considered by Israel's attorney-general, into the alleged appointment of cronies to a government-funded business authority.

His troubles could weigh heavily on Washington's new push to revive Israeli-Palestinian peacemaking, efforts that it hopes can bolster Palestinian President Mahmoud Abbas in his power struggle with the governing Islamist group Hamas.

Mushir al-Masri, a senior Hamas legislator said in Gaza that investigations against Olmert and Halutz's resignation ''prove the Zionist government is weak'' and should spur Palestinians ''to continue resistance and jihad''.

STORM CLOUDS An Israeli poll published on Friday indicated Olmert's approval ratings had slipped to 14 percent. The survey showed his centrist Kadima party would lose nearly two-thirds of its strength in an election.

Balloting is still three years away but storm clouds are gathering quickly on Olmert's political horizon.

A government-appointed commission of inquiry into Israel's inconclusive war against Lebanon's Hezbollah guerrillas is looking into the conduct of Olmert and Peretz in the 34-day conflict that ended in a ceasefire on Aug. 14.

The Winograd Committee's interim report is expected to be out within weeks. Halutz, 58, chose not to wait.

In his resignation letter, Halutz said that after overseeing the military's own investigations into the war, it was time for him to ''act responsibly'' and go. Olmert ''reluctantly accepted'' Halutz's decision, a government official said.

The internal probes criticised Israeli top brass for poor organisation but stopped short of recommending that Halutz quit.

Few in Israel had expected him to remain at his post after a conflict in which the Middle East's mightiest military failed to stop constant Hezbollah rocket attacks that forced a million Israelis to spend a sweltering summer in bomb shelters.

''Never has an Israeli chief of staff resigned of his own free will over the failure of a war,'' Alex Fishman, a military affairs correspondent, wrote in the Yedioth Ahronoth daily.

Israel drove Hezbollah fighters from its northern border but failed to retrieve two soldiers, whose abduction by the group on July 12 triggered the war in which some 1,200 Lebanese, mostly civilians, and 157 Israelis, most of them soldiers, were killed.

Many in Israel questioned whether Halutz, as a former air force chief, had relied too heavily on air power and should have mounted a stronger ground thrust in the early stages of the war.

Halutz, who was appointed chief of staff in 2005, will continue in his role until a new army chief is named. Israel Radio reported Peretz was expected to present a candidate to the government on Sunday.

REUTERS MS HT1530