Police and prosecutors said they asked the Israeli leader during questioning on Friday to "give his account about suspicions of serious fraud and other offences", which involved him billing different public bodies for the same trips abroad.

Police questioned Olmert for the third time on Friday as part of an investigation into allegations he took bribes from American businessman Morris Talansky. Olmert has said he did nothing wrong in his dealings the New York Jewish fundraiser but has promised to step down if formally indicted.

The investigation could hamper U.S.-backed peace talks between Israel and the Palestinians if Olmert is forced to quit.

"According to the suspicions, during his tenure as Jerusalem mayor and trade and industry minister, Olmert would seek duplicate funding for his trips abroad from public bodies, including from the state, with each of them requested to fund the same trip," the statement from police and prosecutors said.

Police suspect Olmert's travel agency issued multiple invoices for trips then transferred the surplus money into a bank account in his name which it managed on his behalf. The funds were used for Olmert's private trips, the statement said.

Olmert's spokesman Mark Regev repeated the prime minister was "convinced of his innocence", which he said would become apparent as the investigation continued.

Olmert was mayor of Jerusalem for 10 years until 2003. He later served as a cabinet minister before succeeding Ariel Sharon as prime minister in early 2006.

The prime minister averted a coalition crisis over the affair when he agreed to hold a party leadership election after Defence Minister Ehud Barak's Labour Party, Olmert's main partner in the government, called on him to step aside.

On Thursday, the Kadima party confirmed that it would hold a leadership election in September which Olmert's deputy, Foreign Minister Tzipi Livni, appears favoured to win, a newspaper survey showed on Friday.

The corruption scandal, which police and judicial sources say involves hundreds of thousands of dollars in questionable cash payments over a decade from the early 1990s, broke two months ago when detectives moved at short notice to question Olmert on May 2.

In testimony on May 27, Talansky told the Jerusalem District Court that he had passed $150,000 (75,600 pounds) to Olmert over a 15-year period, including loans that were never repaid. Olmert said the money was used legally to fund election campaigns.

Olmert's lawyers plan to cross-examine Talansky starting on July 17 in court hearings expected to last several days.