JERUSALEM, July 20 (Reuters) - Lawyers for Prime Minister Ehud Olmert highlighted in court on Sunday inconsistencies in testimony given by a U.S. businessman who told investigators he had given the Israeli leader cash-stuffed envelopes.

Olmert's attorneys cross-examined a visibly weary Morris Talansky, 75, for a third day in a Jerusalem court in a bid to portray him as an unreliable witness. His testimony could be key to any decision to indict Olmert in the corruption investigation.

A New York-based fundraiser for various Israeli organisations, Talansky testified in May that he had given $150,000 in cash-stuffed envelopes to Olmert, the former Jerusalem mayor, over a 15-year period.

Both Olmert, who has pledged to resign if charged, and Talansky have denied any wrongdoing.

In the latest court session, Olmert's attorneys played video clips from police interrogations that showed Talansky changing his account of sums he said he had given to the veteran politician.

Asked to explain the discrepancies, Talansky said they stemmed from "a state of confusion and fear" during police questioning -- and he insisted figures he had given originally had been accurate.

"I'd appreciate if you didn't call me a liar," Talansky told Olmert attorney Eli Zohar after the lawyer asked whether his testimony "is a truth, or a lie".

Olmert, who has been playing up prospects for peace with the Palestinians as the investigation against him heats up, has described funds he received from Talansky as legal contributions to election campaigns before he became prime minister in 2006.

Olmert's own party, Kadima, has begun the process of replacing him. It has scheduled a leadership election for September, under pressure from its main coalition partner, the Labour Party, to get rid of Olmert.

Olmert has pledged to conduct the government's business as usual, despite many Israelis feeling that he will have to step down and speculation about a general election as early as November.

Last week, Olmert, who has been questioned three times by police, was stung by a new set of corruption allegations.

Police said they were investigating suspicions that Olmert made duplicate claims for overseas travel expenses while serving as Jerusalem's mayor and trade minister. His lawyers said he had done nothing wrong. (Writing by Jeffrey Heller, Editing by Ibon Villelabeitia)

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