Sharm el Sheik, Egypt ? President Bush, taking the lead in the frustrating search for Mideast peace, pledged Monday to work unstintingly for the goal of Israel and a Palestinian state living side by side without bloodshed. He said that “this is going to be a difficult process” but claimed progress.

Bush was likely to win support from Arab leaders at a summit today for countering terrorism and for his peacemaking effort. But Arab acceptance of Israel remains conditional on Israel yielding all the land it won in the 1967 Mideast war. That includes part of Jerusalem.

The United States also was trying to narrow differences between Israel and Palestinian leaders before Bush meets with them Wednesday in Jordan.

Israel wants the Palestinians to refer in their statement to a Jewish state. And the Palestinians want Israel to specifically endorse the establishment of a Palestinian state.

On the explosive security front, meanwhile, a compromise was taking shape, with Israel apparently willing to settle for a cease-fire now, provided the Palestinians confront terror groups and uproot them at a later stage. Palestinian leader Mahmoud Abbas contends his authority is not broad enough yet to take on the militants directly.

Bush, following a path that has turned into dead ends for other presidents, began his first trip to the Middle East with a stop at this Red Sea resort. He will meet today with Abbas and the leaders of Egypt, Saudi Arabia, Jordan and Bahrain.

The United States is seeking Arab commitments to strengthen Abbas’ credibility and raise his stature, hoping to marginalize Yasser Arafat, the longtime Palestinian leader who Bush says is untrustworthy.

“I know we won’t make progress unless people assume their responsibilities,” Bush said. “The first message is: I will dedicate the time and energy to move the process forward. And I think we’ll make some progress. I know we’re making progress.”

Arriving at night, the president was greeted at the airport by Egyptian President Hosni Mubarak. Bush wrapped his arm around him in a hug. Mubarak signaled his acceptance of the U.S. formula for peace by inviting Abbas instead of Arafat to the summit.

Bush’s first foray into the complicated world of Mideast negotiations poses a sharp test of the skills of a president whose mastery of foreign policy has been doubted at times. The president had resisted involvement in Mideast peace efforts but promised allies earlier this year that he would plunge in after the Iraq war.

Secretary of State Colin Powell said the summit was important to demonstrate Arab support for the road map and show that Arab leaders will be “speaking out as strongly as I expect the Palestinians to do in denouncing terror and violence and any support that is given to those that practice terror and violence.”

Today’s meeting will be followed by another summit in Jordan on Wednesday with Abbas and Israeli Prime Minister Ariel Sharon, Israel’s most prominent hawk. Powell called the two days of talks a “window of opportunity” to build momentum for ending 32 months of bloody Mideast violence and launching the U.S.-sponsored “road map” that envisions a Palestinian state by 2005.

Bush flew here from Evian, France, where he cut short his participation at the annual summit of industrialized nations by a day to turn to peacemaking.

At an appearance with French president Jacques Chirac, Bush spoke of the Mideast and said “my country and I will put in as much time as necessary to achieve the vision of two states living side by side in peace.”

The pursuit of Middle East peace has stymied American presidents for decades. Bill Clinton traveled to the region a half dozen times and devoted the closing days of his presidency to the search for a settlement. An agreement seemed within reach but then collapsed when Arafat and then Israeli Prime Minister Ehud Barak turned away.

Bush’s Mideast visit follows earlier stops in Poland, Russia and France. He will wrap up his trip on June 5 by visiting U.S. troops in Doha, Qatar, the forward U.S. command post from where the Iraq war was managed.