That despite a row between the president and a Democratic leader back home who made critical comments about U.S. foreign policy.
Mr. Bush and Blair spoke after their meeting at Chequers, Blair's country estate. They called each other by their first names and Mr. Bush pledged to stay in touch with the prime minister.
Mr. Bush and Blair played down U.S.-European differences over missile defense, saying they agree on the need to consider how to deal with security threats posed by the spread of dangerous weapons.
Mr. Bush said he appreciates that Blair, unlike other leaders, is willing to consider new approaches to defense.
Blair, who like most European leaders has been cool to the proposed U.S. anti-missile system, said Mr. Bush had taken the right approach by consulting with allies and recognizing the security threat posed by nations such as North Korea, Iraq and other so-called rogue nations.
Mr. Bush's planned missile defense system, intended to thwart attacks by hostile states, may require the upgrading of U.S. radar facilities at Fylingdales in northern England.
The U.S. plan has triggered unrest in Blair's Labor Party, as well as Britain's European Union partners, who fear it could wreck international nuclear arms control agreements.
Blair noted that he is awaiting a specific missile defense proposal from the United States. Mr. Bush praised Blair for giving his idea a fair hearing. "It's hard for any country to commit to vague notions," Bush said.
On global warming, the two leaders alluded to differences but chose not to dwell on them. Mr. Bush said their nations share a goal of reducing greenhouse gases, and the United States wants to ensure that any solution does not hurt the U.S. economy.
"Our strategy must make sure that working people in America aren't going out of work," Mr. Bush said. "My job is to represent my country, and I'm going to do so in a way that keeps in mind the ability for people to find work and for our nation to be prosperous. I think economic growth and sound environmental policy can go hand in hand."
Mr. Bush has received criticism in Europe for abandoning the 1997 Kyoto global warming pact, which delegates from 180 countries are trying to salvage at a summit in Bonn this week.
Mr. Bush and Blair also discussed efforts to implement a peace agreement for Northern Ireland. Mr. Bush said he supports efforts by Blair and Irish Prime Minister Bertie Ahern to get paramilitary groups to disarm in compliance with the 1998 Good Friday accord.
Earlier, the White House strongly rejected omments by Senate Majority Leader Tom Daschle, who told USA Today that he think the U.S. is "isolating" and "minimizing" itself, reports CBS News White House Correspondent Mark Knoller.
Mr. Bush suggested Daschle's remarks were out of line. "The world leaders have found that I'm a person who speaks plainly and openly about key issues. We're willing to listen," he said.
His top aides went further. Condoleezza Rice called Daschle to discuss the remarks. Bush spokesman Ari Fleischer said Daschle's comments were "a real violation of a long-standing tradition of bipartisanship in foreign policy, particularly during a major foreign trip by the president."
Daschle admitted Thursday that the timing of his comments might have been inappropriate.
"Had I given some thought to the fact that the president was departing I probably would have chosen a different time, but having said them, I will not back away from my comments," he said.
Also Thursday, the Bushes visited the British Museum and headed to Buckingham Palace for cocktails and lunch at Buckingham Palace with Queen Elizabeth II and her husband, Prince Philip.
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