JERUSALEM (Reuters) - Israeli Prime Minister Ehud Olmert admitted on Thursday that he took cash from an American businessman but refused to resign over a police investigation into hundreds of thousands of dollars of alleged bribes.

Israel's Prime Minister Ehud Olmert delivers a speech during a Memorial Day ceremony commemorating fallen soldiers at the Mount Herzl military cemetery in Jerusalem May 7, 2008. REUTERS/David Silverman/Pool

As Israelis enjoyed festivities marking Independence Day and the 60th anniversary of the founding of their state, police lifted a week-old media gag order and announced details of accusations that sparked calls for Olmert to quit.

Whether he does or not, doubt over his future is likely to upset his faltering, U.S.-sponsored peace negotiations with the Palestinians and will cast a heavy cloud over next week’s celebratory visit to Israel by U.S. President George W. Bush.

The White House said Bush still intended to make the trip.

Olmert, in a late-night, televised address to the nation, said: “I look each and every one of you in the eye and say, ‘I never took bribes. I never took a penny for myself’.”

With Olmert’s allies complaining of a campaign to wreck the peace process, it was unclear if his fragile coalition would rally behind a man who last year said he was “indestructible”.

Israelis are no strangers to tales of corruption at the top in the Middle East’s most feted democracy.

Olmert has weathered a string of investigations since he succeeded the ailing Ariel Sharon as prime minister in 2006. Sharon’s son is in jail at the moment for campaign funding misdeeds on his father’s behalf.

On Thursday, Olmert said all the cash he received -- put at hundreds of thousands of dollars by one judicial source -- was legitimate support from New York financier Morris Talansky to fund various election campaigns over nearly a decade from 1993.

“I was elected by you, the citizens of Israel, to be prime minister. I do not intend to shrug off this responsibility,” he said. “However, although not required by law, if the attorney general decides to file an indictment against me I will resign.”

Olmert, 62, said he did not believe the attorney general, with whom he has long been at daggers drawn, would follow through and indict him on the latest accusations.

CAMPAIGN FUNDS

In a terse six-minute address, Olmert said Talansky funded his two successful campaigns for mayor of Jerusalem in 1993 and 1998, an unsuccessful bid to lead the right-wing Likud party in 1999 and a further internal Likud election in 2002. He also said the American “helped me cover deficits” after elections.

Just minutes earlier, police said in a statement: “The investigation deals with suspicions that the prime minister received significant sums of money from a foreigner or number of foreign individuals over an extended period of time.”

A police spokesman named Talansky as a key witness, along with Olmert’s long-time secretary Shula Zaken, who has been under house arrest, and his former law partner Uri Messer.

One police source said investigators cracked coded notes kept by Zaken that they suspect recorded sums given by Talansky -- referred to in some of the notes as “The Laundry Man”.

Palestinian negotiators fear a collapse of the Olmert coalition will scupper hopes for a deal on a Palestinian state before Bush leaves office in January.

If Olmert did step down, however, he could be succeeded by his deputy in the centrist Kadima party, Foreign Minister Tzipi Livni, who has been working closely with Washington and Palestinian negotiators on the peace process.

One lawmaker from Kadima, founded by Sharon and Olmert when they left Likud, said she was “uncomfortable” about the story of money for the party leader. But Ronit Tirosh added that she thought Olmert was capable of continuing to lead the country.

But Gideon Sahar, an ally of Likud chief Benjamin Netanyahu, said: “Olmert is unworthy and cannot carry on in his post. The Kadima government is sunk up to its neck in corruption.”

There was no immediate comment from Livni or from Defence Minister Ehud Barak, leader of Olmert’s main coalition partner the Labour party. Barak is under pressure from some Labour members to bolt the alliance, but others in the party fear that would trigger an election which Netanyahu could win with ease.

Talansky said in Jerusalem that he had given evidence to police after he came to Israel last month to visit relatives for the Passover holiday: “I never was involved in politics,” he said, smiling and joking with Israeli reporters.

“Everything is OK. I don’t understand what’s the big thing.”

Official documents show that Talansky was treasurer of a charity, the New Jerusalem Foundation, which Olmert set up in 1999. U.S. tax records show that this institution declared more than $855,000 in donations from 1999 to 2002.