"Important progress" toward implementing the "road map" for Mideast peace was made in a meeting Wednesday with Israeli Prime Minister Ariel Sharon and new Palestinian Prime Minister Mahmoud Abbas, President Bush (search) said in Jordan.
"The journey we're taking is difficult, but there is no other choice," Bush said at a press conference following a meeting with the foreign leaders. "No leader of conscience can accept more months and years of humiliation, killing and mourning. I know that peace can finally come."
The meeting was the first the three leaders have held together. The White House is clearly pleased with the results of the president's first summit with the two prime ministers, but Secretary of State Colin Powell said the real test will come from performance.
"There will be no military resolution to this conflict," Abbas (search) said after the summit, denouncing terrorism against Israelis and promising to "act vigorously" against incitement and hatred against Israel, including using Palestinian security forces.
"The armed intifada must end and we must use and resort to peaceful means in our quest to end the occupation and suffering of Palestinians and Israelis," he added. "It is time to bring all this suffering to an end."
In a monumental announcement, Sharon (search) said Israel will "immediately" begin to remove unauthorized residential outposts in the West Bank and Gaza strip. Stopping all settlement construction is a major element of the peace plan. Sharon is expected to dismantle about 20 of the 140 settlements.
"There can be no compromise against terror, and Israel, together with all free nations, will continue fighting terrorism until it's final defeat," Sharon added. "We will work with the Palestinians and other states to fight terrorism."
He said the road map provided "hope for a new opportunity for peace" between the two regions, and accepted the principle of a Palestinian state.
Israel released scores of Palestinian prisoners in advance of the summit.
But Abbas said there must be a "clear improvement" in the lives of Palestinians and they must be able to conduct a "normal life" without fear of falling victim to further terror attacks.
Abbas also publicly acknowledged Israel's right to exist side by side with a Palestinian state.
But some militant groups said shortly after the leaders' public appearance that they won't give up their arms or make concessions, and some opponents of the peace plan are calling it the "road map to hell."
An official from Hamas (search), which uses terroristic tactics to protest the existence of an Israeli state, repeated after the press conference that it will not lay down its arms despite appeals from Abbas for all terror groups to do so.
"We are going to continue our resistance until we achieve our goal," senior Hamas official Abdel-Aziz al-Rantissi told Fox News. "Believe me, we will not give up one centimeter of Palestine."
In a sign of the passions that fuel the conflict, a radical Palestinian group urged Abbas "not to bow to Sharon's blackmail and to adhere firmly to the need for equal commitments from the two sides."
The Democratic Front for the Liberation of Palestine urged Abbas to reject "the Israeli and U.S. preconditions that would turn the road map into a mere paper in the drawers of Sharon's government."
Nonetheless, Bush was optimistic after the summit, which also included King Abdullah II of Jordan, who hosted the meeting.
"The holy land must be shared between the state of Palestine and the state of Israel, living at peace with each other and with every nation in the Middle East. All sides will benefit from this achievement and all sides have responsibility to meet," Bush said.
Bush said both sides must make "tangible, immediate steps" to implement the road map, including halting terrorism for good. "We expect both parties to keep their promises."
For his part, Jordan's King Abdullah promised that the world is ready and willing to help the two countries resolve their differences, "but at the end of the day, it is you, the Palestinians and Israelis, that have to come together to resolve the many outstanding issues that divide you.
"Let us have ambitions -- ambitions to move beyond the violence and the occupation," Abdullah said during the press briefing. "In our hands today, we hold the mechanism that can translate these ambitions into realities on the ground."
Wednesday's meeting followed a summit the day before in Egypt, in which Arab leaders agreed to staunch the flow of money to terror groups and committed themselves to making sure the road map is implemented.
"We shall continue to work for a Middle East that is free of strife and violence, living in harmony without the threat of terrorism or dangers of weapons of mass destruction," Egyptian President Hosni Mubarak said Tuesday, reading a statement on behalf of himself, Abbas and the leaders of Jordan, Bahrain and Saudi Arabia. They met with Bush at Sharm el-Sheik, an Egyptian resort on the Red Sea.
Armed militant attacks have killed more than 750 Israelis in the latest round of violence that started when Palestinian militants launched an intifada in September 2000. About 350 died in homicide bombings. During the same period, more than 2,350 Palestinians have been killed by responses from the Israeli military.
Arab recognition of Israel's right to exist and normalized relations are important elements of Bush's peace plan, which envisions a Palestinian state by 2005.
Palestinian residents of the West Bank and Gaza Strip wish to claim those areas for a permanent homeland. Jordan and Egypt lost those territories to Israel during the Six Day War in 1967. Sharon's government has agreed to dismantle some Israeli settlements built in those territories but wants to retain others.
From the summit, Bush flew to Doha, Qatar, visiting U.S. troops in the forward U.S command post where the Iraq war was managed.
The Associated Press contributed to this report.