President Bush, who says peace in the Middle East is one of the prime objectives of his presidency, is sitting down with Palestinian leader Mahmoud Abbas for some of the hard work it will take to turn those words into action.

Bush’s meeting Wednesday was a show of support for Abbas’ moderate politics and his standing in the peace process, even though Abbas was weakened by the victory of rival Hamas militants in parliamentary elections earlier this year.

The Bush-Abbas meeting comes on the same day that the United States and other would-be Mideast peacemakers hold their first session since this summer’s fighting between Israel and Hezbollah militants in Lebanon.

The U.N. Security Council also plans an open meeting Thursday that is intended to revive the peace process.

Abbas was meeting Bush at the Waldorf-Astoria hotel, where the president spent two nights while in town for the U.N. General Assembly.

Bush concluded his formal remarks there Tuesday by calling for the world to support long-elusive peace between the Israelis and Palestinians. Bush held up Abbas’ commitment to peace and a Palestinian state.

"Helping the parties reach this goal is one of the great objectives of my presidency," Bush said.

"I’m optimistic that by supporting the forces of democracy and moderation, we can help Israelis and Palestinians build a more hopeful future and achieve the peace in a Holy Land we all want," Bush said.

He challenged Hamas to reject terrorism, recognize Israel’s right to exist, honor existing agreements and work for peace.

Hamas is sworn to Israel’s destruction. Abbas has been trying to persuade Hamas leaders to moderate their anti-Israel policies and join with his Fatah Party in a coalition government.

U.S. officials have been concerned that Abbas has not shown greater leadership, while Fatah leaders complain that the United States has done next to nothing to support Abbas.

After the Hamas-led Cabinet took office in late March, the United States and European Union, the two biggest donors to the Palestinian Authority, cut off hundreds of millions of dollars in aid. Abbas wants to resolve the political stalemate in hopes of restarting the flow, but discussions have stalled over the U.S. demand that Hamas fully renounce violence, recognize Israel and agree to abide by commitments made by the previous secular Palestinian leaders.

Abbas met Monday in New York with Israeli Foreign Minister Tzipi Livni, the first working session between high-ranking Israeli and Palestinian officials in four months. Afterward, Livni said Israel wants to reopen a serious dialogue with Abbas and work with him to establish a Palestinian state.

The U.S.-backed peace plan aimed to establish a Palestinian state by 2005, but Israel and the Palestinians have failed to carry out their obligations and it has languished.

The efforts for peace were further set back this summer after militants allied with Hamas tunneled from the Gaza Strip into Israel to kidnap an Israeli soldier. The attack, which came after Israel withdrew last year from the Gaza Strip, sparked a large military offensive in the Palestinian area in which more than 200 Palestinians have been killed, most of them militants.

Days later, Hezbollah guerrillas abducted two soldiers in northern Israel and killed three others, triggering a larger assault across the border into Lebanon that lasted a month.

Bush planned to return to Washington after his meeting with Abbas.

Copyright © 2006 The Associated Press