Despite his condolences for the Palestinian people, President Bush's (search) few words over Yasser Arafat's (search) death belie his distaste for the terrorist-turned-patriarch of the Palestinians. Instead, the president is focused on the possibility of a peaceful future in the Middle East.

Bush welcomed British Prime Minister Tony Blair (search) to the White House just before 7 p.m. — the two leaders shaking hands and then quickly walking inside without speaking to reporters on the objectives of their two days together.

On Friday, Bush also met with Blair, who after Bush's re-election last week said forging an Arab-Israeli peace is the single most pressing political challenge in the world today.

He echoed the thought before leaving London for Washington.

"We have a situation where it's a huge problem of discontent and problems within the world so it is important we deal with it," he said.

Blair's own party members say Bush owes the prime minister for his strong support for the war in Iraq (search). But U.S. experts say Europe can't lead the way to a Mideast peace.

"The Israeli people and the Israeli leadership see the United States as their friend in good times and bad. They do not trust the Europeans in that way," said former ambassador Martin Indyk.

As Yasser Arafat lay dying, Bush met Wednesday evening with Muslim leaders to mark the holy month of Ramadan (search), which ends this weekend. While there, he spoke of his hopes for peace and focused on leaders on the ground who could help.

"By working with leaders in that region, we can advance reform and change in a vital part of the world," Bush said.

Bush never believed that Arafat was a leader who would work for peace. A man who first proposed terror as a solution when he was 18 years old, Arafat spent 40 years trying to get rid of Israel before agreeing in principle to a two-state solution. But Arafat never changed the charter of the Palestinian Liberation Organization (search) he founded that called for the destruction of Israel and he returned to war four years ago.

In a written statement after hearing of Arafat's death, the president tersely called it "a significant moment in Palestinian history."

Indyk agreed. "Yasser Arafat had become like this great boulder in the middle of the road blocking implementation of the road map and any chances for moving forward in the negotiation," he said.

Former President Clinton, who tried to forge an Israeli-Palestinian peace, also acknowledged Arafat's shortcomings. He said in a statement that "Palestinians saw Arafat as the father of their nation, but he missed the opportunity to bring that nation into being."

With Arafat's death, however, comes hope. The United States is offering to help with Palestinian elections, and placing its bets on two men who also found it hard to work with Arafat.

Mahmoud Abbas lasted four months as Arafat's prime minister and left in a dispute over control of security forces. Ahmed Qureia took over the post, but was unable to exert much authority.

Indyk says the good news is the two leaders are favored by the right segments.

They have legitimacy within the mainstream nationalist movement of the Palestinians. They are opposed as well by Hamas.

Indyk said Israel has killed so many leaders of the Hamas terror group, that the organization is weakened and its opposition is less of a concern. However, U.S. support also isn't much help to the men because the Arab world believes the United States is biased toward Israel.

Blair, however, says European leadership in the Mideast peace process could be the key, and he argues that an end to the Arab-Israeli dispute could help quash global terrorism.

"Because there's misery for Palestinians, there's misery for Israelis who suffer terrorist activity, and in the meantime, we have a situation where it's a huge problem of discontent and problems within the world, so it is important we deal with it," he said.

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