(Adds Rice quotes, paragraphs 6, 11-12, changes dateline)

By Arshad Mohammed

JERUSALEM, March 26 (Reuters) - The United Nations raised the idea of gathering Israel, the Palestinians and Arab states at a meeting to try to revive peace talks as U.S. Secretary of State Condoleezza Rice on Monday shuttled between the sides.

The intensified diplomacy comes ahead of an Arab summit expected to relaunch a Saudi-backed peace plan calling for Israel to quit all occupied Arab lands in exchange for peace.

Israeli Prime Minister Ehud Olmert said he would "not hesitate to participate" if invited to an expanded meeting of the Quartet of Middle East mediators that could also include Saudi Arabia.

A public meeting that brings Israeli and Saudi officials together would be a breakthrough. The countries do not have formal relations, though there have been reports of informal Saudi contacts with Olmert.

U.S. officials said the idea was only one of several being considered and no decisions had been made.

"The only decision that has been made by the Quartet is that we will meet at some point in the region. Precisely what geometry we might use has not really been decided or really fully considered by the Quartet or by other parties," Rice told reporters before meeting Israeli Foreign Minister Tzipi Livni.

The Quartet is made up of the United Nations, the United States, the European Union and Russia.

During a brief visit to Amman, Rice met for a second time in 24 hours with Palestinian President Mahmoud Abbas, and held talks with Jordan's King Abdullah. She later returned to Jerusalem for a second round of talks with Olmert.

Rice met separately on Sunday with Abbas and Olmert to see if they would agree to talk about peace indirectly, with the United States shuttling back and forth, rather than face-to-face.

On her fourth visit to the Middle East in four months, Rice is talking to the two sides separately because Olmert has so far ruled out engaging Abbas on peace since the Fatah leader formed a unity government with the Islamist Hamas.

STICKING TO ROAD MAP

Analysts doubt she can make much progress given Olmert's political weakness -- one opinion poll this month showed he would win as little as 3 percent of the vote if an election were held immediately -- and the Palestinian divisions.

While pressing her idea of "parallel talks" Rice denied she was trying to pre-empt direct Israel-Palestinian contacts.

"I don't intend by any means to take control of the Palestinian-Israeli bilateral dialogue. I think it's extremely important that that continue," she said.

Rice has also 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 Arab foreign ministers agreed on Monday that this week's Arab summit would revive an Arab initiative for peace with Israel without any amendments.

U.N. Secretary-General Ban Ki-moon, 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.

"It is a very interesting, useful idea to consider. But we need more consultations," Ban said.

At a press conference in Jerusalem with Ban, Olmert said he would continue his contacts with Abbas and said 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 its terms.

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