The two leaders stood by their decision to invade Iraq
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The US and British leaders have defended the war against Iraq and insisted the decision to topple Saddam Hussein was based on good intelligence.
Tony Blair and George W Bush met briefly at the White House after the UK prime minister made a speech to a joint session of Congress.
One of the issues they said they would discuss was that of British detainees held by the US at Guantanamo Bay, and a statement is expected on Friday.
Mr Blair - who was greeted with cheers and repeated standing ovations during his address - said that even if they had been wrong about weapons of mass destruction, history would forgive the removal of Saddam Hussein.
Although Mr Blair received a rapturous welcome in Congress, it was not entirely a victory celebration, says the BBC's Rob Watson in Washington.
In both capitals, doubts about the intelligence underpinning the need for war are proving hard to dispel.
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Mr Blair is preparing the ground for a fresh justification for war in the event WMD never turn up
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President Bush said the ousted Iraqi leader Saddam Hussein "produced and possessed chemical and biological weapons, and was trying to reconstitute his nuclear weapons programme."
He said that when all the speculation was over the truth would come out - that the intelligence against Iraq had been good.
Mr Bush has now distanced himself from allegations about attempts by Iraq to buy uranium in Niger, but Mr Blair expressed faith in Britain's sources for the claims.
"Let me just say this on the issue to do with Africa and uranium. The British intelligence that we have we believe is genuine. We stand by that intelligence," he said at a news conference held after his speech to Congress.
Fight against terrorism
In his speech, Mr Blair urged the US and Europe not to allow their differences over the invasion of Iraq to interfere with the fight against international terrorism.
He said humanity would not forgive world leaders if they failed to combat the threat, which he described as a new and deadly virus whose capacity to inflict pain had been enlarged by technology.
The aim of the fight against terrorism and - in the case of Iraq - weapons of mass destruction, was to unify the world through liberty which, he said, was not a western value but a universal one.
"Can we be sure that terrorism and weapons of mass destruction will join together? Let us say one thing. If we are wrong, we will have destroyed a threat that, at its least, is responsible for inhuman carnage and suffering. That is something I am confident history will forgive."
Hearts and minds
He praised Mr Bush's leadership, saying: "There never has been a time when the power of America has been so necessary and so misunderstood."
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BLAIR'S FAR EAST TOUR
1. Tokyo
2. Seoul
3. Beijing
4. Shanghai
5. Hong Kong
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Mr Blair's visit to Washington marks the start of an eight-day trip which will see him go on to Tokyo, Japan; Seoul, South Korea; Beijing and Shanghai in China
and Hong Kong.
And he assured him that Britain would stand by the US "in the fight for liberty".
But he called on the US to "listen as well as lead" in order to win hearts and minds around the world.
Mr Blair also said terrorism would not be defeated until there was peace between Israel and the Palestinians, saying that it was there that "the poison was incubated".
He called for Israel's security to be respected and for the creation of a viable Palestinian state.