U.S. Secretary of State Condoleezza Rice said at a farewell U.N. appearance Monday that Israel and the Palestinians have moved much further along the path to peace since President George W. Bush brought their leaders together a year ago — though they won't clinch an agreement by the end of the year.

Rice spoke to reporters after a meeting of the diplomatic Quartet of Mideast peacemakers — the U.S., the U.N., the European Union and Russia — which said the Israeli-Palestinian negotiating process launched by Bush at Annapolis, Maryland "is irreversible" and should be intensified to "establish as soon as possible the state of Palestine."

The Annapolis agreement called for the Israelis and Palestinians to try to end their decades-long conflict and sign a peace agreement by the end of 2008, which would have given Bush a diplomatic victory just before turning the presidency over to Barack Obama.

"They won't achieve agreement by the end of the year, but they have achieved a good deal of progress in their negotiations, a good deal of progress in the work that is being done on the ground," Rice said.

"This is the first time in almost a decade that Palestinians and Israelis are addressing all of the core issues in a comprehensive way to try to get to a solution, and if that process takes a little bit longer, so be it," she said. "But we are very much further along, certainly than we were in 2001, and I would argue even than in 2007 when Annapolis was concluded."

The United States and Russia — which have recently been at odds — have joined forces to cosponsor a U.N. Security Council resolution which would also declare the support of the U.N.'s most important body for the Annapolis process "and its commitment to the irreversibility of the bilateral negotiations."

The council is scheduled to meet Tuesday to adopt the resolution, which U.S. officials said has very wide support.

"I believe that will then add the voice of the international community, through its most powerful and its most consequential body, that is the Security Council, to establish ... the Annapolis process as the way forward," Rice said.

Rice's two-day U.N. visit was aimed not only at firming up her boss' imprint on the Mideast peace process but to press for tougher measures against Somali pirates and focus on other global hotspots including Zimbabwe, Congo and Iran.

The Security Council is also expected to vote Tuesday on a U.S. resolution that would authorize "all necessary measures" against piracy from Somalia, including hunting pirates ashore, despite the commander of the U.S. Navy's 5th Fleet expressing doubt Friday about the wisdom of launching attacks against Somali pirates on land.

U.N. Secretary-General Ban Ki-moon hosted a farewell dinner Monday night in Rice's honor.

The U.N. chief thanked the outgoing U.S. administration, especially Bush and Rice for their "tireless" efforts to advance Israeli-Palestinian negotiations since the Annapolis agreement.

"Very important progress is under way," Ban said. "We are united in our conviction that it must be continued and intensified in the period ahead. In this respect, we look forward to working closely from the outset with the administration of President-elect Obama to achieve the goal of a two-state solution and comprehensive Arab-Israeli peace."

The Quartet statement stressed that a final treaty and lasting peace will be reached "through simultaneous and mutually re-enforcing efforts" on three tracks: negotiations, building the institutions of a Palestinian state, and implementation of the parties' obligations under the roadmap to peace.

It called for an extension of the Egyptian-brokered "calm" in Gaza, which expires later this month, condemned indiscriminate attacks from Gaza against Israel, and expressed "acute concern" at Israel's closure of crossing points in response to the violence which has curtailed the delivery of essential humanitarian supplies to Gaza.

The Quartet also called on the Palestinians to continue efforts to reform their security services "and dismantle the infrastructure of terrorism," and on Israel to freeze all settlement activities and "address the growing threat of settler extremism."

After the Quartet meeting, its members meet with the foreign ministers of Saudi Arabia, Jordan, Bahrain, the United Arab Emirates and Morocco, Arab League chief Amr Moussa, and ambassadors from other Arab nations.

Saudi Foreign Minister Saud Al-Faisal told reporters afterwards that the Arab peace plan, which calls for Arab recognition of the Jewish state in exchange for a full Israeli withdrawal from all lands captured in the 1967 Mideast war, "is still on the table and it is a generous offer that deserves a reply."

"We don't want negotiations for the sake of negotiations," he said. "We want results, and regretably, we were not able to achieve any breakthrough in any of the fundamental issues such as borders, withdrawal and settlements."

Israel objects to relinquishing all territory and the right of all Palestinians to return, and it wants to keep a unified Jerusalem as its capital. But Saud has said the plan is a package that can't be divided.

Russia's Foreign Minister Sergey Lavrov said the resolution to be voted on Tuesday is aimed at creating two states, Israel and Palestinians, living side by side in peace.

"It is aimed at continuing our joint efforts and implementing them, taking into account the recent reaffirmation by the Arab League of the Arab peace initiative which we view as having great capacity," he said.