(Adds Olmert, Hadley comments, paragraphs 6-7, 11)

By Jeffrey Heller and Matt Spetalnick

WASHINGTON, June 4 (Reuters) - U.S. President George W. Bush told Israeli Prime Minister Ehud Olmert on Wednesday Iran posed an "existential threat to peace" the world must take seriously.

The White House talks came a day after Olmert, on a U.S. trip while under criminal investigation at home, issued his toughest warning yet to Iran, saying its nuclear program must be stopped by "all possible means."

Echoing Israel's frequent description of a nuclear-armed Iran as a risk to its survival, Bush said at the start of the meeting: "It is very important for the world to take the Iranian threat seriously, which the United States does."

Israel, widely believed to be the Middle East's only nuclear weapons power, regards Iran as its chief regional foe.

Bush has led a campaign of international sanctions against Iran, which insists its nuclear program is strictly civilian.

At Bush's side in the Oval Office before their private talks, Olmert said Iran poses "the main threat to all of us."

"Each passing day, we are taking another significant step to deal more effectively with this problem," he told reporters after the meeting. "When I say each passing day, that includes today," he said alluding to his talks with Bush.

Olmert's visit occurred at a time when he is facing calls for his resignation over a corruption scandal that could disrupt Bush's already-flagging Israeli-Palestinian peace effort.

The two leaders took no questions in the Oval Office, avoiding potentially embarrassing inquiries about Olmert's legal and political woes.

They also discussed the peace efforts launched in November at an international conference in Annapolis, Maryland. But in their statements to reporters, neither leader repeated the goal of reaching a deal, including agreement on Palestinian statehood, before Bush leaves office in January, a deadline viewed with broad skepticism.

Bush's national security adviser Stephen Hadley said after the meeting that the "parties still seem committed to trying to reach an agreement this year." Olmert echoed that sentiment telling reporters, "I hope we can reach decisions in 2008."

In the occupied West Bank, Palestinian chief negotiator Ahmed Qurie said it would take a "miracle" to meet that target. Bush hopes the peace bid would grant him a foreign policy legacy defined by more than the unpopular war in Iraq.

Peace prospects have dimmed amid violence on Israel's border with the Gaza Strip that is controlled by Islamist Hamas, Israeli settlement construction in the West Bank and the criminal investigation of Olmert.

The Israeli leader faces calls to resign over court testimony that he took cash-stuffed envelopes from a Jewish-American businessman. Olmert admits taking the money but described it as legitimate contributions to election campaigns before he became prime minster. He has said he would step down if indicted.

Olmert's tough words toward Iran during his three-day visit that ends on Thursday only briefly shifted media focus in Israel away from his troubles at home.

Iranian President Mahmoud Ahmadinejad said earlier this week Israel would soon "disappear off the geographical scene," his latest in a series of verbal attacks on the Jewish state. (Additional reporting by Jeremy Pelofsky; Editing by Frances Kerry, Alan Elsner, Jackie Frank)

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