President Bush (search) said Wednesday he is hopeful about Mideast peace negotiations with new Palestinian leaders. Bush spoke before Palestinian leader Yasser Arafat's (search) death Thursday in a hospital outside Paris.

Against the backdrop of strong American support for Palestinian moderators already designated for top roles, Bush said, "There will be an opening for peace when leadership of the Palestinian people steps forward and says, 'Help us build a democratic society."'

"And when that happens — and I believe it's going to happen because I believe all people desire to live in freedom — the United States of America will be more than willing to help build the institutions necessary for a free society to emerge so that the Palestinians can have their own state," Bush said.

He spoke after a White House meeting with Jaap de Hoop Scheffer (search), the secretary-general of the North Atlantic Treaty Organization.

After his own meeting with the former Dutch foreign minister, Secretary of State Colin Powell (search) stressed peace prospects rest heavily on whether a new leadership makes it clear it will fight terrorism and "will not in any way give any kind of support to terrorist activities."

Also, Powell said, the new leaders must be able to "mobilize the Palestinian people to bring them together to the realization that terrorism is not helping them achieve their desire for a state of their own, a desire that all of us share."

"If that kind of leadership emerges," Powell said, "then we stand ready to work with them."

The first president explicitly to endorse the establishment of a Palestinian state on land now held by Israel, Bush renewed that pledge immediately after his re-election last week.

In the same vein, he said Wednesday: "The vision is of two states, a Palestinian state and Israel living side by side, and I think we've got a chance to do that, and I look forward to being involved in that process."

Bush shunned Arafat from the outset, refusing to invite him to the White House. He sent Secretary of State Colin Powell to talk to Arafat on the West Bank. Eventually, those contacts dwindled and were cut off when the Bush administration concluded Arafat was inept and had not done enough to stop attacks on Israel.

In June 2002, Bush urged the Palestinians to replace Arafat with leaders "not compromised by terror."

Arafat died Thursday morning in France. He had spent his final days in a coma at a French military hospital.

Palestinian Prime Minister Ahmed Qureia and former Prime Minister Mahmoud Abbas are expected to play leading roles in transition. They are considered moderate and to have tried, unsuccessfully, to persuade Arafat to get tough on terrorism.

Gearing up for new Palestinian leadership, the United States has conveyed its strong support for elections within 60 days of Arafat's death.

The elections, which are called for under Palestinian law, are viewed by Washington as a way of ensuring a legitimate transfer of authority to new leaders with the hope they would take charge of maintaining order and nurturing a nascent Palestinian government.

Powell on Tuesday discussed the transition with Nabil Shaath, the Palestinian foreign minister, during a telephone call from Mexico City, where the secretary was meeting with Mexico officials.

"Our interest is in seeing smooth arrangements. And they appear to be being made and carried out. And we hope that the calm and the kind of orderly processes prevailing will continue," State Department spokesman Richard Boucher said Wednesday.

Powell and Shaath "didn't get into the questions of who might attend whatever ceremonies or funerals there might be," Boucher said.

Plans are being made for a funeral in Cairo and burial in Ramallah, on the West Bank, where Arafat made his headquarters.

Among the possibilities for U.S. representation are a low-level official from the U.S. Embassy in Egypt or the U.S. consulate in Jerusalem, which deals with the Palestinians.