WASHINGTON — President Bush tried today to reassure Israelis worried about the American commitment to keeping Iran from obtaining nuclear weapons.

“Iran is an existential threat to peace,” Mr. Bush told Prime Minister Olmert at the outset of talks at the Oval Office. “It’s very important for the world to take the Iranian threat quite seriously, which the United States does.”

Mr. Bush said they also would discuss Syria’s influence in Lebanon and the Israeli government’s attempts to negotiate peace with the Palestinian Arabs. As they spoke, The president of the Palestinian Authority, Mahmoud Abbas, called for a new dialogue with Hamas, the militant group that has taken control of the Gaza Strip from Mr. Abbas’ government. Mr. Abbas said he will call for new legislative and presidential elections if the talks succeed.

Neither Mr. Bush nor Mr. Olmert mentioned perhaps the most pressing issue for their talks: Mr. Olmert’s deteriorating political situation back home, where his popularity has nose-dived because of a new corruption scandal, and the end of his term is largely seen as just a matter of time. The developments are jeopardizing Mr. Bush’s already ambitious timetable for a peace agreement between Israel and Palestinian Arabs by year’s end and are making it unlikely that Mr. Bush or Mr. Olmert will be able to shepherd the process to completion.

For Mr. Olmert, a friendly meeting with a stalwart ally like Mr. Bush was a marked change from what he left behind in Israel, where his political allies are conspicuously refusing to come to his defense and jostling for his job.

The Israeli leader seemed delighted to be again at the side of Mr. Bush, who is enormously popular in Israel. Mr. Olmert smiled broadly at Mr. Bush throughout his opening remarks and effusively praised his speech last month before the Israeli Knesset.

“The people of Israel were absolutely excited and moved by your spectacular speech at the Knesset, which was the best expression of the United States’ commitment to the security and the well-being of the state of Israel,” Mr. Olmert said.

Mr. Bush’s emphasis on Iran, which came unprompted, reflects its importance to Israel. Both countries are concerned about Tehran’s intentions, but Israel has a different intelligence assessment on the state of Iran’s nuclear program. Israel believes that Iran has not suspended its nuclear weapons program, despite a report to the contrary by American intelligence.

In an indication of what Mr. Olmert was likely to tell Mr. Bush, the Israeli prime minister told thousands of Israel supporters at the annual convention of the American Israel Public Affairs Committee yesterday that the Iranian threat “must be stopped by all possible means.”

Mr. Olmert said international sanctions aimed at stopping Iran from developing nuclear weapons must be ratcheted up urgently, and he suggested measures like banning Iranian businessmen and financial transactions and imposing sanctions on Iran’s crucial import of gasoline.

Mr. Olmert said the world should see that “the long-term cost of a nuclear Iran greatly outweighs the short-term benefits of doing business with Iran.”

But sanctions are “only an initial step,” and Iran’s flouting of the international measures so far “leave no doubt as to the urgent need for more drastic and robust measures,” Mr. Olmert said.

Israeli newspapers also have reported that Mr. Olmert hopes to acquire a sophisticated American missile defense system, advanced radar, and new warplanes.

The discussion of Syria comes against a backdrop of Israel’s renewed peace talks with Damascus, which happened last month without the involvement of America, which has tried to isolate the regime. Syria’s president said in interviews published yesterday in the United Arab Emirates that America would have to become involved if the process is to succeed.

The Bush administration has become deeply involved in Israel-Palestinian Arab peace negotiations. Mr. Bush set the target for a peace agreement at the end of the year, saying Mr. Olmert and Mr. Abbas are the right people to lead a historic compromise.

But the administration now seems aware that Mr. Olmert could be on his way out. The peace process between Israel and Palestinian Arabs “is bigger than any one person, and we’re going to continue to work on it, despite what may or may not be happening in Israeli political circles,” White House press secretary Dana Perino said.

Speaking at the Aipac annual conference, Mr. Olmert made only one oblique reference to his domestic woes, mentioning that he briefly considered calling off his visit to America because of “the recent political developments in Israel of which you are aware.”

Mr. Olmert was addressing the group of powerful American Israel supporters just as his relationship with one such supporter threatens to ignominiously end his term in office. The testimony of a New York businessman, Morris Talansky, who claims to have given Mr. Olmert envelopes stuffed with cash over a decade and a half, in part to fund a lavish lifestyle, has thrown Israel’s political system into turmoil.

Mr. Olmert’s key coalition partner, the defense minister, Ehud Barak, now says he’ll topple the government if Mr. Olmert doesn’t step aside. And Mr. Olmert’s rivals in his Kadima Party, including his popular deputy, the foreign minister Tzipi Livni, are jostling for position and gearing up for party primaries.