(Adds Talansky quote to judge)

JERUSALEM, July 18 (Reuters) - The U.S. businessman at the centre of a corruption case against Ehud Olmert told a court on Friday he was worn out from questioning by the Israeli prime minister's lawyers, saying "I can't do it anymore".

Olmert's lawyers challenged Morris Talansky's memory about funds he raised and accused him of lying during a second day of cross-examination in the Jerusalem District Court.

"You are inventing a story and I pity you," Eli Zohar, one of Olmert's lawyers, told Talansky.

Talansky 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.

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.

Appearing tired and sometimes exasperated, Talansky, 75, appealed to the court for the questioning to end on Sunday, two days earlier than planned.

Talansky said he wanted to return to the United States to be with his wife, who is sick. Talansky said he would be back in Israel in September and could be cross-examined then.

"I simply don't have the energy ... to stay more than Sunday," he told the three-judge panel. "My wife, my life and business is absolutely in shambles because of this. This has just worn me out... I can't do it anymore."

The court rejected the request.

Olmert, who has been playing up prospects for peace with the Palestinians, has described the funds he received from Talansky 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, to show he an unreliable witness.

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.

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 said the government's business carries on as usual, despite many Israelis feeling 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 whether Olmert had made duplicate overseas travel expenses claims while Jerusalem's mayor and trade minister. His lawyers denied any wrongdoing. (Writing by Adam Entous; Editing by Matthew Jones)

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