Near the end of a visit to Israel in January, President Bush had some parting advice for senior members of its government: "Take care of Olmert."

He had reason to worry. Israeli Prime Minister Ehud Olmert, his partner in pursuing peace with the Palestinians, is the unpopular and vulnerable leader of a fractious coalition.

"Israeli politics is like karate," Bush observed, according to participants at the private dinner. "You never know when the next chop will come."

As Bush returns to Israel today, Olmert's job looks less secure than ever. The latest blow is a corruption scandal that broke last week and threatens to paralyze a U.S.-backed peace process that is already limping.

Israel's police fraud unit has raided government offices, seized files and interviewed Olmert and dozens of witnesses in a widening probe. The investigation focuses on suspicion that the Israeli leader received hundreds of thousands of dollars in illicit cash from 1993 to 2005 from Morris Talansky, a wealthy New York businessman described by one investigator as "Olmert's ATM."

Olmert, who denies taking bribes and says the money was used for legitimate campaign expenditures, has promised to step down if indicted.

That sets up two scenarios, either of which could frustrate Bush's goal of at least a partial peace agreement by the end of his presidency: If the investigation drags out, Olmert could remain under suspicion for the rest of this year, constrained in his political authority to make peace. If it ends quickly in an indictment, the struggle to succeed him would consume Israel for months, putting peace talks on a back burner.

Olmert is a skilled political survivor who has weathered several other corruption investigations stemming from events before he became prime minister in 2006. He has not been formally charged and rejects the suspicions that he used Cabinet positions and his decade as Jerusalem's mayor to improperly change rules, influence decisions or benefit business and party associates.

The latest inquiry is viewed as more serious. Unlike the others, it involves allegations of envelopes stuffed with cash as well as testimony from the giver and an alleged accomplice, Olmert's legal counsel, concerning transfers.

"It looks like the most flagrant kind of corruption," said Moshe Negby, a prominent legal analyst.

According to a poll of Israelis this week, three of five respondents disbelieve Olmert's denial and want him to resign. Sensing his vulnerability, senior members of his centrist Kadima party have begun jockeying to succeed him as the party's leader. Several politicians have an eye on replacing him as prime minister.

Foreign Minister Tzipi Livni, Israel's chief negotiator in talks with the Palestinians, is first in line to become prime minister but faces strong rivals within Kadima.

Defense Minister Ehud Barak, another contender, could bring down the government by pulling his left-leaning Labor Party from the governing coalition.

But neither party is eager to force an early election because polls show that opposition leader Benjamin Netanyahu of the Likud party, a right-wing critic of the peace process, is Israel's most popular politician.

By pledging to resign if indicted, Olmert appears to have bought time until police finish collecting evidence and Atty. Gen. Menachem Mazuz decides how to proceed.

That will allow Olmert to promise Bush this week that he will keep working to end the conflict. Olmert said Tuesday that he and Palestinian Authority President Mahmoud Abbas had reached "understandings and points of agreement" on some issues, but he gave no details.

Bush, who is to hold two private meetings with Olmert during a 48-hour visit, told Israeli journalists at the White House that he considers the Israeli leader "an honest guy" but sidestepped questions about his ally's longevity in office.

"It's a legal matter inside the system," Bush said, adding that negotiations to create an independent Palestinian state do not hinge only on Olmert. "This is a plan of a government."

Since Bush launched the latest round in November, the talks have produced few signs of progress on the main issues of borders, the fate of Palestinian refugees and conflicting claims to Jerusalem. Palestinian leaders have criticized Olmert's government for not making enough good-faith gestures, such as removing security checkpoints or halting expansion of settlements in the West Bank.

But Palestinian negotiator Saeb Erekat said Olmert's political demise would make things worse.

"If he's out and they go to early elections," Erekat said, "that means peacemaking is on hold for a year."

How much time Olmert has to make a deal depends on the attorney general.

In disclosing the investigation last week, the Justice Ministry did not say what specific crime was suspected, what Talansky's money was meant for or what favors, if any, the businessman allegedly got in return. Depending on evidence, legal experts say, Mazuz could try for a relatively quick indictment for campaign finance violations or build a slower case for the more serious charge of bribery.

But Menachem Hofnung, a Hebrew University political scientist, says limits on donations a candidate can receive were so complex and changed so frequently during the period under investigation that it would be hard to prove a violator's criminal intent.

In either case, prosecutors would have to notify Olmert of any charges they were considering, give his lawyers access to the evidence and conduct a preliminary hearing before an indictment could be brought.

"Based on experience, that could take up to six or seven months," said Zeev Segal, a Tel Aviv University law professor.

Columnist Uzi Benziman says Olmert may have lost the ability to lead. "His position has been undermined. He is incapable of leading the state into battle, just as he is incapable of reaching a peace agreement," Benziman wrote in the newspaper Haaretz.

"If he tries to initiate anything, the criminal investigation will be exploited to undermine his authority to make or implement decisions."