JERUSALEM — Israel’s popular foreign minister said today that the ruling party must prepare to replace Prime Minister Olmert, raising pressure on him to step down amid a growing corruption investigation.

Calls for Mr. Olmert’s ouster grew this week after the key witness in the case, an American businessman, Morris Talansky, described handing tens of thousands of dollars to Mr. Olmert, in part to finance the Israeli politician’s expensive tastes. The foreign minister, Tzipi Livni, was the first senior member of his own Kadima Party to question his fitness to stay in office.

“I think the reality has changed since yesterday and Kadima has to make decisions,” Ms. Livni told reporters in Jerusalem. “I suspect that Kadima needs to start right away acting for every eventuality, including elections.”

Ms. Livni said she favored holding a party primary to give the public a say in choosing a leader.

“In this way, we can operate to restore the trust in Kadima,” she said, without mentioning Mr. Olmert by name.

Opinion polls show Ms. Livni to be the country’s most popular politician, and she would stand a good chance of winning a nationwide party primary. However, she faces many rivals among the party’s leadership, and there is no guarantee she would win a contest decided in a smaller forum.

Yesterday, the defense minister, Ehud Barak, called on Mr. Olmert to step aside, pledging to pull his Labor Party, a key coalition partner, out of the government and force new elections if the Israeli leader didn’t comply.

“The die has been cast,” Mr. Barak told a meeting of his Labor Party at Tel Aviv. “We should prepare for elections … in my estimation we are going to elections, it could be before the end of this year.”

Mr. Olmert has denied wrongdoing and said he would resign only if he is indicted. He has not commented publicly about Mr. Talansky’s testimony and tried to maintain a business-as-usual appearance.

Today he hosted the the prime minister of Denmark, and his office released a busy schedule of events for next week, including a trip to Washington to meet President Bush.

Mr. Olmert has weathered a string of scandals since he took office two years ago and has vowed to fight the latest accusations. His lawyers are set to cross-examine Mr. Talansky on July 17.

Mr. Olmert could still hang on to power. With the hardline opposition leader, Benjamin Netanyahu, expected to do well in the next election, both Ms. Livni and Mr. Barak could be reluctant to push harder to force new elections.

Last year, Ms. Livni called on Mr. Olmert to resign after a government investigation harshly criticized Mr. Olmert’s management of Israel’s war in Lebanon in 2006. But she was criticized for not following through by resigning. Likewise, Mr. Barak never carried out a threat to force Mr. Olmert out after the report.

While it remains unclear whether Mr. Olmert actually violated any laws, Mr. Talansky’s testimony painted the Israeli leader in extremely unflattering terms that could make it difficult to stay in office.

The Justice Ministry said today that investigators are speeding up their corruption probe in an effort to wind up the case. Prosecutors are looking into possible bribery, campaign funding violations, and money-laundering.

No timetable will be set for concluding the investigation when the attorney general, Meni Mazuz, meets later today with police and prosecutors, a ministry spokesman, Moshe Cohen, said. But “there is an overriding public interest to wind this thing up quickly,” Mr. Cohen said. “This is not a regular investigation.”

In court on Tuesday, Mr. Talansky said he gave Mr. Olmert $150,000 of his own money over the years, in addition to unspecified sums from other donors. Mr. Olmert insisted on getting the money in cash, and used it to help finance his penchant for high-living, including luxury hotels and first-class travel, Mr. Talansky told the court.

The outcome of this latest political crisis could have a profound effect on the fate of Israel’s peacemaking with Palestinian Arabs, and on talks with Syria, recently relaunched after breaking down eight years ago.

The White House press secretary, Dana Perino, said today that Mr. Olmert’s political trouble “obviously takes up some oxygen” when it comes to negotiating Middle East peace, but that it’s a matter of internal Israeli politics.

She said Mr. Bush plans to meet with Mr. Olmert when he is at Washington next week.

Recent polls have shown that Mr. Netanyahu of the Likud Party, who takes a hard line against the Arabs, stands a good chance of winning, making already fragile peace prospects even more questionable.

Washington has been prodding Israel and the Palestinian Arabs to try to conclude a blueprint for a peace deal by the end of his tenure in January. Yesterday, a State Department spokesman, Tom Casey, declined to speculate on the possible effect of a change in leadership on the American-backed peace process.

“I’ll leave it to the Israelis to have their own internal political debate and discussions,” Mr. Casey said. “We are committed to continuing to work with both sides to move the peace process forward, and that’s what we’re going to continue to do.”

Corruption allegations have clung to Mr. Olmert throughout his three-decade political career. The latest investigation is the fifth into his affairs since he was elected two years ago.

The president of the Palestinian Authority, Mahmoud Abbas, has said publicly that he considered the matter an internal Israeli issue. But his aides have said they are worried about the effect Mr. Olmert’s woes will have on peacemaking.

Turkey-mediated talks with Syria were only disclosed last week, and there has been no comment from Damascus on Mr. Olmert’s troubles.