In his last visit to the United States as British prime minister, Tony Blair said Thursday that tough-questioning reporters, protesters and opposition leaders can all criticize the choice to go to war, but he and President Bush stand by their decision to invade Iraq.

"We took a decision that we thought was very difficult. I thought then, and I think now, it was the right decision. History will make a judgment at a particular time," Blair said in his 16th trip to the United States since Bush became president.

"But one thing I know is that what we represent coming here today, speaking in the Rose Garden to you people and getting your questions and being under your pressure, that is a finer and better way of life than either a brutal, secular dictatorship or religious extremists. It's a better way of life and it's the way of life actually people, any time they are given the choice, choose to have," he said.

Bush and Blair, whose 10-year term as head of government in the United Kingdom ends on June 27, agreed that the relationship between the United States and Great Britain is bigger than the personalities who lead the country.

"This relationship is one that is vital to accomplish big objectives. It has stood the free world — it has enabled the free world to do hard things. It's a relationship that I believe is necessary to do the hard things in the 21st century," Bush said.

In an impassioned rebuttal that began with a reporter asking about Conservative Party leader David Cameron's decision to avoid coming to Washington, D.C., Blair said it's not his place to give advice to the opposition party, but he and Bush are battling for the values that enable their opponents to criticize them.

"You don't win those battles by being a fair-weather friend to your ally. You don't win those battles by being hesitant or withdrawing support for each other when the going gets tough. You don't win those battles by losing the will to fight if your enemy's will to fight is very strong and very powerful," he said.

"People run down politics and say it's all just a series of positions and attitudes and sound bites and occasionally lies and all the rest of it. And you see, what politics is in the end, when it's done in the right way and people stand up for what they believe, it's about public service and there's nothing to be ashamed of in that. And what we should be about, our two nations, is giving as many people in the world as possible that choice, and being proud of it," Blair continued.

Both leaders have suffered at home as a result of their joint venture into Iraq. But Blair's popularity in the United States remains high. According to a FOX News-Opinion dynamics poll taken May 15-16, Blair has a 64 percent favorability rating among the 900 registered voters surveyed. In the latest poll, Bush's favorability rate rose to 41 percent, with a 54 percent unfavorable rating.

During their 45-minute press conference, the president, who has frequently been buoyed by having a staunch ally make his case for coalition action in Iraq, heaped warm praise on the prime minister.

"My relationship with the leader of Great Britain has been very productive and I have enjoyed working with Tony Blair more than I could have possibly imagined. It is hard to define a relationship in sound bites or press conferences in a way that really reflects the depth of what we have done together," Bush said.

Blair has been an able leader, "since 1797," Bush joked at the outset of their question-and-answer session, referring back to a recent flub he made during Queen Elizabeth II's visit earlier this month. Blair took office in 1997.

Bush did not ascribe Blair's decision to step down to his own unpopularity in Britain, but said he hopes to help Britain's new prime minister, Gordon Brown, "the way Tony Blair helped me."

"[I was a] newly elected president, Tony Blair came over, he reached out, he was gracious. He was able to converse in a way that, where our shared interests are the most important aspect of the relationship. I would hope I would provide the same opportunities for Gordon Brown," Bush said.

Blair expressed appreciation for the alliance he and Bush maintained in their six and a half years working together and warned that the two nations cannot let their resolve fizzle when it comes to fighting Al Qaeda in Iraq and elsewhere.

"If what happens is the harder they fight, the more our will diminishes, then that's a fight we're going to lose. And this is a fight we cannot afford to lose," Blair said.

"The relationship between the United States of America and Great Britain is a relationship that is in the interest of our two countries and in the interest of the peace and stability of the wider world, and sometimes it's a controversial relationship, at least over in my country, but I never doubted its importance, I never doubted that it's based on principle, shared values and on a shared purpose," he added.

In a bit of domestic scuttlebutt, Bush praised Senate and House Democratic leaders for moving a step closer to an Iraq war spending bill that they pledged to get to the president's desk by Memorial Day. But he said he "refused to negotiate from" the podium, and was leaving talks to his chief of staff Josh Bolten.

"We're working hard. I think we can get a deal. We fully understand the need to have benchmarks in a bill. I respect the members' desire for benchmarks. After all, I am the person who laid them out initially," he said.

Bush said that during their meeting at the White House, he and Blair discussed Iraq, Iran, Mideast peace, other foreign policy goals such as Darfur, AIDS treatments and education initiatives for Africa, defense trade, climate change and a variety of issues of interest to both leaders. Thursday's meeting is not the last time the two leaders will work together. Blair and Bush are among the leaders to attend next month's G-8 conference of industrialized nations.

"I assured the prime minister we want to be a part of a solution, that we want to work constructively together. ... I've got some good ideas about how to convince China and India to be part of a global solution," Bush said of the challenges to reducing human contributions to global warming.

FOXNews.com's Sharon Kehnemui Liss contributed to this report.