JERUSALEM, July 18 (Reuters) - Israeli Prime Minister Ehud Olmert's lawyers questioned a U.S. businessman at the centre of a corruption case for a second day on Friday, challenging his memory about funds he raised and accusing him of lying.

"You are inventing a story and I pity you," Eli Zohar, one of Olmert's lawyers, told Morris Talansky in the Jerusalem District Court.

Talansky, 75, said there may be lapses in his memory "here or there" but he stood by his testimony in a case that could force Olmert out of office.

Appearing tired and sometimes exasperated during a second consecutive day in court, Talansky appealed for the questioning to end on Sunday, two days earlier than planned.

But the court rejected the request.

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 and Talansky have denied any wrongdoing.

Olmert, who has been playing up prospects for peace with the Palestinians, has described the funds as legal contributions to election campaigns before he became prime minister in 2006. He has said he would resign if indicted.

Olmert's lawyers have focused on poking holes in Talansky's statements to investigators and aim to show that he is not a reliable witness against the prime minister.

Zohar challenged Talansky on Friday on whether donors gave cash or cheques at fundraising meetings.

In his testimony in May, Talansky said that cash and cheques were given. On Friday, he told the court only cash was given.

"Again, the lie," Zohar responded at one point.

Talansky said his accounts in general were accurate.

"This is over a 10 year period and you ask me to remember every part?" Talansky asked.

The next court session will be on Sunday.

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 Adam Entous; Editing by Elizabeth Piper)

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