But that solution, following the death of Palestinian leader Yasser Arafat (search), can only be achieved if both states vow to pursue democratic paths, the two allies said.
"Israelis and Palestinians living side by side in peace and security" is the goal, Bush said in a White House press conference with Blair. "Our sympathies are with the Palestinian people as they begin a period of mourning," Bush continued, adding that the months ahead offer an opportunity to secure "lasting peace."
"I don't think there will ever be lasting peace unless there is a free, truly democratic society in the Palestinian territories," he added. The president said responsibility rests with not only the Palestinian people, but also with the incoming leadership, Israelis and the free world to help pursue a democracy-fostering strategy.
"We'll hold their feet to the fire to make sure that democracy prevails," Bush said of the Palestinians' onus to elect a democratic government.
Blair vowed that "we will do is anything necessary to make this strategy work," but that strategy must include coming to an agreement on what a viable Palestinian state means.
"What we're saying this morning is, that viable state has to be a democratic state," Blair said. "We will do whatever it takes to help build support for that concept."
With Arafat's death, the future of the Middle East peace process has taken center stage. The so-called roadmap for peace calls for a new Palestinian state in 2005. Britain is concerned that Israel's proposed withdrawal from Gaza will create a destabilizing power vacuum if the Palestinians are not ready to assume control.
After Bush's re-election last week, Blair said forging an Arab-Israeli peace is the single most pressing political challenge in the world today.
Asked point blank during Friday's press conference whether it was the goal of his second term to see two states emerge living side by side, Bush responded: "I think it is fair to say that we have a great chance to establish a Palestinian state and I intend to use the next four years to spend the capital of the United States on a Palestinian state. I believe it's in the interest of the world that a truly free state develop."
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 (search) lasted four months as Arafat's prime minister and left in a dispute over control of security forces. Ahmed Qureia (search) took over the post, but was unable to exert much authority.
"There is a two-state solution based on the fact that they have to first stop terrorism before there is a state," said Raanan Gissin, a spokesman for Israeli Prime Minister Ariel Sharon. "Bush is putting it as a challenge to the future Palestinian leadership. ... He says 'It's up to you and you have a new situation.' ... The fact is that there is a new era now. He is urging them to drop the Yasser Arafat legacy."
Israel's foreign minister, Silvan Shalom, will fly to Washington to meet on Monday with Secretary of State Colin Powell. Shalom said this week that the new Palestinian leadership "will have to prove itself" before a peace process can go forward.
The president sounded cool about the prospects of attending an international conference on Middle East peace. "I'm all for conferences," he said, "just as long as a conference produces something."
Among the other topics the two leaders were expected to discuss were trans-Atlantic relations, which were frayed by the invasion of Iraq; spreading democracy throughout the Middle East; Iran's nuclear program; conflicts and poverty in Africa; and climate change.
Iraq, Middle East Progress is Hard Work
Both leaders acknowledged that not only was achieving peace among Israelis and Palestinians not going to happen overnight but neither was democracy in Iraq or Afghanistan -- but that by no means implied it can't be done.
"I think it's unrealistic to say, 'well Bush wants it done and Blair wants it done so it's gonna happen,'" Bush said, noting that post-World War II, no one ever thought Japan and the United States, nor Germany and the United States, would be friendly and that democracy would take root in those two overseas countries.
"It's hard and it's difficult, particularly in a society like Iraq because the terrorists understand the stakes of freedom and they're willing to kill people in brutal fashion to stop it," Bush said. "I believe we have a duty and obligation to make sure democracy takes hold."
He warned that with upcoming Iraqi elections, "the desperation of the killers will grow and the violence could escalate." But he said victory in Iraq would be a blow to terrorists everywhere.
Blair said that in a post Sept. 11, 2001, world, it's no longer just good enough to rout out terrorists in countries like Iraq and Afghanistan but what's needed is the establishment of new, democratic governments run by a free people.
"I think what we are learning today …stability of any true, long-term kind [cannot be had] without democratic rights and free people to decide their government," the British leader said. "It's a struggle. Democracy is hard to bring to countries that have never had it before but I have no doubt at all that the Iraqi people, given the chance, will want to elect their leaders … why wouldn't they?"
"We're not going to have our security unless they get that freedom," he continued.
The London press has called Blair the "poodle" of Bush, insinuating that the British official has been a Bush lackey, especially in regards to Iraq. There's been rumoring that Blair is now looking for a sense of payback from Bush and that that payback could be in the form of a commitment to the Middle East peace process.
"The prime minister made the decision he did [to ally itself with the United States in Iraq] to make sure" the British people were safe from terrorists, Bush countered. "He's very capable of making up his own mind - he's a strong, capable man … when he says something, he means it … he's a big thinker ... when times get tough, he doesn't wilt … what this world needs is steady, rock solid leaders."
Blair said the concept of payback is nonsense.
"We're not fighting the war against terrorism because we are an ally of the United States -we are an ally of the United States because we believe in fighting this war against terrorism. We share the same objectives, we share the same values," he said.
"I believe we should be thankful it [the U.S.-U.K. relationship] is as strong as it is today and as long as I remain prime minister of our country, it will carry on being strong ... because I believe passionately, it is in the interest of Britain."
Other issues on the table for Bush and Blair to discuss on Friday include:
-Iran. Blair wants Bush to allay European fears that the United States would take military action against Iran. The United States wants Iran dragged before the U.N. Security Council to face sanctions, claiming the Persian state is trying to build nuclear weapons. Iran contends its nuclear program is peaceful and aimed at generating energy.
-Climate change. Blair would like Bush to soften his rigid opposition to the Kyoto international climate treaty, which goes into effect early next year without U.S. participation. Expressing concern about U.S. jobs, Bush is holding fast to his rejection of the treaty, which requires industrial nations to reduce emissions of so-called greenhouse gases below 1990 levels.
The Associated Press contributed to this report.