A public meeting that brings Israeli and Saudi leaders together would be a breakthrough. The countries do not have formal relations, though there have been reports of informal Saudi contacts with Olmert.
During a brief visit to Amman, Condoleeza Rice, the US secretary of state, met for a second time in 24 hours with Mahmoud Abbas, the Palestinian president, as well as with Jordan's King Abdullah. She will return later to Jerusalem for further talks with Olmert.
Rice met separately on Sunday with Abbas and Olmert to gauge the chances for peace talks but said she was not striving for a "big bang" breakthrough.
On her fourth visit to the Middle East in four months, Rice is talking to the Israelis and Palestinians separately because Olmert has so far ruled out engaging Abbas on peace since the Fatah leader formed a unity government with the Hamas party.
Rice has been encouraging Arabs to revive the peace plan they ratified in 2002 by adding what she calls "active diplomacy" - seen as code for early contacts with Israelis.
But Jordan said that Arab foreign ministers agreed on Monday that this week's Arab summit would revive an Arab initiative for peace with Israel without any amendments.
Ban Ki-moon, the UN secretary-general, also on a visit to the region, said on Monday that Israeli and Palestinian leaders, along with officials from Saudi Arabia, Egypt, Jordan and the United Arab Emirates, could be invited to attend the next Quartet meeting, expected to take place in Egypt.
Ban said: "It is a very interesting, useful idea to consider but we need more consultations."
"The new government should show signs of maturity and responsibility"
Husky, Ottawa, Canada
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The United Nations is part of the Quartet, whose other members are the United States, the European Union and Russia.
At a press conference in Jerusalem with Ban, Olmert said he would continue his contacts with Abbas and that a long-stalled "road map" peace plan "will be the basis for advancement here between us and the Palestinians".
Neither the Israelis nor the Palestinians have fulfilled their commitments under the road map, which calls for Israel to halt settlement building in the occupied West Bank and the Palestinians to dismantle militant groups.
The 2002 plan touted by Rice, known as the Saudi initiative, offers Israel normal ties with Arab countries in return for full withdrawal from land it occupied in the 1967 Middle East war.
Olmert urged Arab states to advance the proposal but Israel has said it cannot accept some of the terms.
Israel and the Quartet have demanded the Palestinian government recognise Israel, renounce violence and accept existing peace deals.
The new unity administration has agreed to "respect" previous accords and renounce civilian violence but has stopped short of formally recognising Israel or giving up the "right of resistance" under international law.
Analysts doubt Rice can make much progress given Olmert's political weakness - one opinion poll this month showed he would win as little as 3 per cent of the vote if an election were held immediately - and the divisions among the Palestinians.