WASHINGTON — When Ehud Olmert announced he was quitting, three of the four people likeliest to succeed him as Israeli prime minister already were auditioning for two of the job’s toughest constituencies: the U.S. government and American Jewry.

Olmert’s timing was notable: Foreign Minister Tzipi Livni and Transportation Minister Shaul Mofaz — both Kadima Party candidates — and Ehud Barak, the defense minister and leader of the Labor Party, all were in Washington last week when the prime minister said he would not run for Kadima’s leadership in September.

They, along with Likud Party leader Benjamin Netanyahu, are vying to succeed Olmert, who is quitting under a cloud of multiple police investigations into allegations of corruption.

In Washington, the question of who would succeed Olmert provoked uncertainty about the future of the signature issues of the U.S.-Israel partnership: U.S.-sponsored peace talks between Israel and the Palestinians, relaunched last year at Annapolis, Md., and isolating Iran until it ends its suspected nuclear weapons program.

Livni was quick to offer assurances that though Israel’s leader is changing, its priorities are not.

“The fact that there are internal changes does not change the fact that a threat exists,” Livni said of Iran after meeting with U.N. Secretary-General Ban Ki-moon in New York. “It doesn’t change the interests of Israel that we are obligated to represent.”

Jewish leaders in the United States publicly expressed confidence that the U.S.-Israel relationship was strong enough to weather the crisis, but privately many wondered whether any of Olmert’s likely successors could match his warm ties both with U.S. Jews and the White House.

Of Israel’s four main contenders, only Livni and Mofaz can run in the Kadima primaries in September to succeed Olmert. But Israel could see new general elections in early 2009 if the winner of Kadima’s primary is unable to assemble a coalition government. In that case, Netanyahu, Barak and others could compete, and Olmert would remain caretaker prime minister into next year, beyond the tenure of the Bush Administration.

New polls taken July 31 in Israel cast Livni as the front-runner. As Israel’s lead negotiator with the Palestinians, Livni is an enthusiastic proponent of Israeli-Palestinian talks and already has pledged to do her best to close a deal before President Bush leaves office in January.

She is well-liked among American Jews, in part for her articulate English skills and because she represents a successful woman politician. Livni also is close with U.S. Secretary of State Condoleezza Rice, with whom she met last week in Washington.

Barak also spent time with Rice last week. He was invited to her home for dinner Tuesday evening, the day before Olmert’s announcement, after spending a day in talks with his U.S. counterpart, Defense Secretary Robert Gates. Rice and Barak are both accomplished pianists, and that was to have been a component of the evening’s entertainment.

In their daytime meeting, however, Rice was all business, extracting a pledge from Barak to do more to facilitate freedom of movement for Palestinians in the West Bank and to cooperate with Gen. James Jones, the U.S. envoy assigned the task of nurturing the Palestinian security force to maturity.

In his meeting with Gates, Barak said that when it comes to threatening the possibility of military action should sanctions fail to cow Iran, “We should mean it when we say it.”

That imperious tone did little to endear Barak to the Clinton Administration during his own stint as prime minister, from 1999 to 2001, although President Clinton did defer to the Israeli leader in the 2000 talks with the Palestinians at Camp David.

Barak told Israeli reporters last week that he missed those days when Israel and the United States tacitly agreed on “contours” before launching peace talks.

It’s not clear a Barak premiership would enjoy the same collaborative relationship with Barack Obama or John McCain as president. Both U.S. candidates have suggested they are likelier to lead than to follow when it comes to Middle East peacemaking.

Mofaz is well liked by the Bush Administration for deferring to its preferences, particularly on Iran, and might be seen as a better alternative than Barak.

In Washington last week, in his capacity as the chief Israeli negotiator in the U.S.-Israel strategic dialogue, Mofaz and his U.S. counterparts released a joint statement July 31 after their meeting: “The United States and Israel share deep concern about Iran’s nuclear program, and the two delegations discussed steps to strengthen diplomatic efforts and financial measures to prevent Iran from developing a nuclear weapons capability.”

If there is a concern about Mofaz, it is his halting English — a deficit that also could hinder his relationship with U.S. Jews.

Seymour Reich, the president of the Israeli Policy Forum and a former chairman of the Conference of Presidents of Major American Jewish Organizations, recalled the difficulties posed by Amir Peretz, Barak’s predecessor as defense minister, whose English also was poor.

“He had difficulty in articulating his concepts and thoughts to our community,” Reich said. “He never overcame that, although he did try hard. Hopefully any successor will be fluent in English and, more importantly, in the idioms and the nuances.”

That has never been a problem for Netanyahu, who was raised in the United States. However, foreign policy officials and Jewish community leaders have mixed feelings about his record when he was prime minister from 1996 to 1999.

Netanyahu was a tough advocate for Israel, but he angered some U.S. Jews when he courted Republicans and evangelical Christians to press Clinton to abandon some of the precepts of the Oslo process. Netanyahu was responsible as well for the sole episode when Israel, rather than the Palestinians, was widely perceived in the United States as reneging on a deal when he failed to withdraw Israeli forces from Palestinian areas after the Wye River agreement in 1998.

Some hawkish Jewish groups last week were seizing on the prospect of a change in Israel’s leadership as a hopeful sign that peace deals they see as too concessionary will be scuttled.

Morton Klein, the president of the Zionist Organization of America, said Olmert’s closeness to Bush was more of a danger than a salve.

“Under the circumstances of a concessionary government like Olmert’s, a good relationship with Bush I don’t think was a great benefit right now,” Klein said.

Klein, however, did credit Olmert with having a sensitive understanding of the Diaspora’s relationship to Israel.

Freezing peace talks now would send the wrong message, Americans for Peace Now warned.

“Israel is engaging on both of these tracks because it is in Israel’s vital interests to do so,” Americans for Peace Now said in an analysis, referring to Israel’s peace talks with the Palestinians and with Syria. “Abandoning these efforts during this transition would be a major, and unnecessary, setback.”