Along with the uncertainty that is expected to accompany the death of Yasser Arafat (search ) is the hope that a new Palestinian leadership may open new lines of communication in the Mideast and perhaps with Washington, D.C.

"There will be opening for peace when leadership of the Palestinian people steps forward and says, 'Help us build a democratic and free society,"' President Bush (search) said Wednesday after an Oval Office meeting with the secretary-general of NATO, Jaap de Hoop Scheffer.

"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.

"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 said.

Committing to a policy he created early in his first term, Bush never met personally with Arafat. Now that Arafat is gone, the time could be right for a new leader who is willing to negotiate peace with Israel.

"Arafat couldn't end the conflict because the conflict defined him," said former Mideast peace negotiator Dennis Ross, who has met with Arafat more than 500 times. "When I said he was the embodiment of the cause, in his own eyes he represented the cause and he couldn't live without it. When we remove him from the equation, as I say, there is uncertainty, but there is also possibility."

The possibility still seems remote for some, as the Israeli-Palestinian conflict has brewed since Israel's creation as a modern nation in 1948. Bush's refusal to talk with Arafat goes back to his father, the first President Bush, who also never met with the Palestinian leader but did meet with Arafat's intermediaries at a 1991 peace conference in Madrid.

The conference led to secret negotiations between Israelis and Palestinians in Oslo, Norway, that President Clinton tried to build on, negotiating a land-for-security deal between Arafat and then-Prime Minister Benjamin Netanyahu in the fall of 1998. But negotiations foundered before Clinton could seal a peace agreement between Arafat and then-Prime Minister Ehud Barak (search ) at a Camp David summit in the summer of 2000.

"They couldn't get there. That's the truth. They couldn't get there," Clinton said in July 2000.

The current President Bush entered office highly skeptical of Arafat's commitment to peace, though more than a year later he was willing to concede Arafat's role in the peace process.

"The president does believe that the path to peace goes through Chairman Arafat," then-White House spokesman Ari Fleischer said in April 2002.

But the Sept. 11, 2001, terror attacks on the United States led to a new Bush foreign policy that precluded talks with terrorists, which as head of the Palestinian Liberation Organization, Arafat was considered long before he was resurrected as a statesman. As Bush's policy matured, Arafat personally lied to the president about 50 tons of Iranian weapons destined for Palestinian fighters that were seized by the Israeli Navy, and he failed to prevent a March 27, 2002, bombing that killed 20 Israelis at a Passover dinner in Netanya.

Arafat's last meeting with a high-ranking U.S. official was in April 2002, when Secretary of State Colin Powell warned the Palestinian leader that relations were headed for a break.

"I've made it as clear as I can to him that we are and have been disappointed with his performance. And it's time for him to make a strategic choice," Powell said.

In June 2002, the president declared Arafat's choice, a refusal to negotiate, was the wrong one.

"Peace requires a new and different Palestinian leadership so that a Palestinian state can be born," Bush said in the Rose Garden.

The decision forced Arafat to name a prime minister, Mahmoud Abbas, and in June 2003, Bush met with Abbas at a summit in Egypt. But the violence between Palestinians and Israelis continued to rage and Abbas quit in September in a dispute over control of security forces.

Arafat chose a new prime minister, Ahmed Qureia, who has yet to meet with the president and has sharply criticized Bush's support for Israeli Prime Minister Ariel Sharon's unilateral security initiatives like the security perimeter being built around Israeli settlements in the West Bank and Jerusalem and targeted attacks on the leadership of Arafat's Fatah group of fighters.

Mideast experts warn the United States will need Arab support to keep other countries from taking advantage of Arafat's death, or "that vacuum being filled by states such as Iran by states such as Syria," as Mideast scholar Rob Sobhani put it.

Problems could also come up from within the Palestinian leadership.

"At least with Arafat you knew what you had — you knew he was a known quantity," said retiring Louisiana Sen. John Breaux. "If there is a real battle to replace him between the moderates and the extremists within the PLO, it could present a very dangerous situation for the United States to have to deal with."

"I would like to see us also focus on elections with an eye toward using them as a device, as a mechanism to resume discussions between Israelis and Palestinians," Ross said. "I would like us ... to call for elections and actually organize negotiations between Israelis and Palestinians because you can call for elections, but you have to have an environment in which they can be conducted."

Aides say the president's ready to work with Palestinians who believe in his vision of a peaceful, two-state solution in the Mideast that has been outlined along with the European Union, the United Nations and Russia.

"We know the way forward, the road map is there, the road map is ready to be used," Powell said.

Aides say the president has not asked his most senior advisers to monitor the Palestinian transition, in part because it is not at all clear that Arafat's successor would be helped by anything that looks like a U.S. endorsement.

Click in the box near the top of the story to watch a report by FOX News' Wendell Goler.