JERUSALEM — Prime Minister Olmert’s lawyers today began cross-examining an American businessman who accused Mr. Olmert of accepting thousands of dollars in cash from him to fund a lavish lifestyle.

The lawyers hope to discredit businessman Morris “Moshe” Talansky’s allegations that Mr. Olmert had illicitly accepted cash-stuffed envelopes to pay for a penchant for expensive cigars, first-class travel and luxury hotels.

Mr. Olmert has denied any wrongdoing and has said he will resign if he is indicted. It may take months before police decide whether to indict Olmert.

In an Israeli courtroom, an Olmert lawyer, Eli Zohar, accused Mr. Talansky of forgetting details or giving inaccuracies.

Mr. Talansky said he might have gotten a few minor things wrong, like the time that events occurred, but that in general he was telling the truth.

“I never gave a false answer,” Mr. Talansky said. He appeared nervous, drumming his fingers on the table, fidgeting with a plastic cup and at one point asking for a break.

In a new blow to Mr. Olmert’s efforts to clear his name, a key member of his defense team, Ron Shapira, has resigned, according to a lawyer on the defense team, Navot Tel-Tzur.

The Haaretz newspaper reported today that Mr. Shapira resigned after he was criticized for suggesting that Mr. Olmert accept a plea bargain, rather than face possible prison time.

Mr. Shapira’s departure was depicted in the Israeli media as a sign of turmoil inside Mr. Olmert’s defense team just as the crucial cross-examination of Mr. Talansky was beginning.

The cross-examination, expected to take five days, is seen as perhaps Mr. Olmert’s last chance at political survival.

Mr. Talansky’s allegations in May seriously damaged Mr. Olmert’s credibility among Israelis and the resulting outrage prompted Mr. Olmert’s Kadima Party to set new leadership elections for September 25.

Mr. Olmert’s premature departure from office could seriously hamper or delay his government’s efforts to conclude a peace deal with the Palestinian Arabs and resume full negotiations with the Syrians.

Mr. Olmert is reportedly still considering running in the Kadima primaries, hoping that his lawyers will be able to discredit the 75-year-old Orthodox Jew who lives on New York’s Long Island but frequently visits family in Israel.

Mr. Talansky accused the prime minister of accepting the cash during Mr. Olmert’s tenure as Jerusalem mayor and as a Cabinet minister before he was elected in 2006. Police suspect the money was meant as bribes — although Mr. Talansky insisted he never got anything in return — or illegal campaign financing.

Mr. Talansky had agreed to the questioning on his own accord and is not suspected of violating any Israeli laws. He has expressed exasperation with the intense media focus on him.

Last week, police accused Olmert of pocketing thousands of dollars by deceiving multiple sources — including organizations for Holocaust survivors — into paying for the same trips abroad. The widening of the investigation was announced as Mr. Olmert was questioned for the third time in the corruption probe.

Mr. Olmert has called the most recent accusations “distorted,” charging that the police and state prosecutors with trying to bring him down. He said he felt insulted because he had worked hard for the organizations named in the allegations, which include the Yad Vashem Holocaust memorial and the Nazi watchdog Simon Wiesenthal Center.

Mr. Olmert’s allies note that he’s been written off before only to emerge intact. This is the fifth major corruption case against him and few thought he’d survive the fallout from his much-criticized handling of the 2006 war in Lebanon.