Bush warned after meeting with Olmert that a nuclear-armed Iran would be an "incredibly destabilising" force, and that if the Islamic republic continued "forward with their programme there has to be consequences."
"If the Iranians want to have a dialogue with us, we have shown them the way forward, that is, for them to verifiably suspend their enrichment activities," Bush told reporters at the White House.
Speaking in Hebrew after the meeting in Washington, Olmert said that "our position is that we must do everything in our power to make sure the Iranians do not cross a technological threshold that would allow them to develop nuclear weapons."
Olmert said that he had had a "deep conversation" with Bush and that the two leaders had "complete understanding over their objectives" regarding Iran.
Backed by the United States, Israel has said sanctions are necessary following Tehran's failure to suspend uranium enrichment.
Israel -- widely considered the Middle East's sole, if undeclared, nuclear weapons power -- considers Iran its chief threat, pointing to calls from President Mahmoud Ahmadinejad for the Jewish state to be wiped off the map.
But the Bush-Olmert summit "was not meant to discuss specific policies, but rather offer the two leaders an opportunity to exchange views on current developments," Israeli officials told AFP.
Earlier on US television, Olmert said he hoped diplomacy would dissuade Tehran from pursuing its nuclear program.
"We will not tolerate the possession of nuclear weapons by Iran," Olmert told NBC television's "Today Show".
Asked whether his country was considering a pre-emptive strike on Tehran's nuclear facilities, Olmert answered: "I hope we don't have to reach that stage."
But the Israel leader said his first choice is a negotiated resolution.
"Every compromise that will stop Iran from acquiring nuclear capabilities, which will be acceptable to President Bush, would be acceptable to me."
Asked what he believed to be the timeline for Iran developing possible nuclear weapons, Olmert responded, "it's a matter of, unfortunately, shorter time than most people think."
"I don't want to measure it in days or weeks, but it's quite close," he said.
Olmert added that he was not seeking Washington's protection from Tehran.
"I am not coming to the United States to ask America to save Israel," he said, saying his country had drawn the lessons of the Holocaust and World War II.
The Israeli leader added: "I am not looking for wars or confrontations. I am looking for the outcome."
He added that, in his view, the only result that matters is "whether it will succeed to stop Iran from possessing nuclear weapons."
On Sunday, Olmert reiterated Israel's position that Iran should be intimidated from the consequences of it completing its nuclear programme, which Israel, the US and European states claim is aimed at building an atomic bomb, despite Iranian claims it is meant for peaceful means only.
"Iran will not agree to make compromises if it is not afraid of the options it would face in the absence of a compromise," Olmert told reporters.
He hinted that "Israel has options which I am not ready to specify" regarding Iran's nuclear programme.
Meanwhile US State Department spokesman Sean McCormack said on Monday Washington no longer sought direct contacts with Iran to discuss ways to ease unrest in neighbouring Iraq, saying that channel of communication "didn't work out".
"We went through a period where there was an offer of that channel of communications," McCormack said. "It didn't work out for a variety of different reasons," he said.

Copyright AFP (Agence France-Presse), 2006