Condoleezza Rice urged Israel on Sunday to be bold in pursuing peace with the Palestinians after Israeli leaders warned her there could be no deal on a Palestinian state until their own security was guaranteed.

In Jerusalem to negotiate on a planned peace conference, the U.S. Secretary of State assured Israeli Prime Minister Ehud Olmert the United States was committed to ensuring Israel's survival and said it was time to take difficult decisions.

Olmert said that despite questions over Palestinian leaders' ability to rein in militants hostile to Israel, he was ready to negotiate on all core issues after the initial conference, to be hosted by U.S. President George W. Bush, and held out the possibility of a breakthrough before Bush steps down next year.

But Rice, who will meet Palestinian President Mahmoud Abbas in the West Bank on Monday, cautioned that it was still too early to set a date for the conference at Annapolis, Maryland. U.S. officials have penciled in the week beginning November 26.

It is time for us all to make difficult decisions for the sake of peace, Rice said in a speech to an audience that included Olmert. All Israelis should be confident that America is fully behind you, that we are fully committed to your security and you can thus be bold in your pursuit of peace.

Earlier, on Rice's eighth visit in a year -- and third in six weeks -- to the region, Israel's chief negotiator told her the situation was more complicated than ever, and said Israel would only accept a Palestinian state if Abbas ensured, under the U.S.-backed road map accords of 2003, that his state posed no threat to Israel.

They need to understand that the implementation of future understandings would be implemented only according to the phases of the road map -- the meaning is security for Israel first and then the establishment of a Palestinian state, Foreign Minister Tzipi Livni told reporters as Rice stood at her side.

Abbas says Israeli occupation hampers his security efforts.

THREATS

Olmert, speaking later at the same event as Rice, noted the threats Israel faced, both in the occupied West Bank where Abbas's Fatah faction holds sway and in the Gaza Strip, which was seized by Hamas Islamists in June. Nonetheless, he said, Israel wanted to take the opportunity Abbas's overtures presented.

We have reasons to delay, he said. But ... we have a partner and we are not willing to delay the negotiations to a time when our partner might be unable to fulfill the task.

If we and the Palestinians act with determination there is a chance of making significant achievements, maybe even before the end of president Bush's term, Olmert added.

Annapolis will be the springboard for continuing serious and intensive negotiations that will not pass over any issue and will avoid no controversy, he said, conceding that Israel too had yet to fulfill its road map commitments. Notable among these is an obligation to rein in Jewish settlement in the West Bank.

Several hundred torch-bearing demonstrators marched nearby to protest at his apparent readiness to discuss dividing Jerusalem between the two states. Some said they opposed any Arab state on land they believed was given to the Jews by God.

Abbas said in Ramallah that the Palestinians had met 90 percent of their commitments and Israel must now do its part.

Rice and Olmert both noted they were speaking on the 12th anniversary of the assassination of Israeli Prime Minister Yitzhak Rabin by a Jew hostile to his plans for peace.

Speaking of a rise of violent ideologies, some sponsored by Iran or linked to al Qaeda, Rice warned that if Palestinian leaders were unable to deliver on hopes for a state then the moderate centre could collapse forever and the next generation of Palestinians could become lost souls of unbridled extremism.

She stressed: Failure is simply not an option.

Israel and the Palestinians are at odds over a joint policy document for the conference, after which they would negotiate on core issues such as borders, the fate of Jerusalem and millions of Palestinian refugees. Israel also opposes Abbas's push for a deadline to conclude a deal, which Abbas would like by August.

(Additional reporting by Adam Entous, Ari Rabinovitch and Eli Berlzon in Jerusalem and Ali Sawafta in Ramallah)