"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 on Sunday.
"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."
Olmert said he was ready to negotiate on all core issues after the initial conference despite raising questions over Palestinian leaders' ability to rein in armed groups.
He also held out the possibility of a breakthrough before George Bush, the US president who is to host the summit, steps down next year.
US officials have tentatively scheduled the summit for the week beginning November 26.
But Rice, who will meet Mahmoud Abbas, the Palestinian president, in the West Bank on Monday, highlighted the difficulty on getting the sides to agree on the agenda, saying it was still too early to set a date for the conference at Annapolis, Maryland.
Israel and the Palestinians are at odds over a joint policy document for the conference, after which they are to negotiate on core issues such as borders, the fate of Jerusalem and millions of Palestinian refugees.
Israel also opposes Abbas's push for an August deadline to conclude a deal.
On Rice's third visit in six weeks and eighth in a year, 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 US-backed "road map" accords of 2003, that his state posed no threat to Israel.
Security then state
"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," Tzipi Livni, Israel's foreign minister, told reporters as Rice stood at her side.
|Hundreds of Israelis demonstrated against |
territorial concessions on Sunday [AFP]
Abbas said in Ramallah that the Palestinians had met "90 per cent" of their commitments and Israel must now "do its part".
Olmert, speaking at the same event as Rice, noted the threats Israel faced but said: "We have a partner [Abbas] and we are not willing to delay the negotiations to a time when our partner might be unable to fulfil 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 said the Annapolis talks would be the "springboard for continuing serious and intensive negotiations that will not pass over any issue and will avoid no controversy", conceding that Israel had yet to fulfil its road map commitments, including to rein in Jewish settlement in the West Bank.
Several hundred torch-bearing demonstrators marched nearby to protest against his apparent readiness to discuss dividing Jerusalem between the two states.
Olmert and Rice noted they were speaking on the 12th anniversary of the assassination of Yitzhak Rabin, the then Israeli prime minister, by a Jew against his plans for peace.