UK Prime Minister Tony Blair has said the invasion of Iraq will have been vindicated, even if no weapons of mass destruction are found.
Bush and Blair praised each other's leadership
The British leader was addressing the United States Congress in only the fourth speech there by a UK prime minister. He was greeted with cheers and 17 standing ovations.
Mr Blair warmly praised the US, saying "being American means being free," but he also warned the US it must listen.
At a news conference afterwards, US President George W Bush also defended the war against Iraq.
He said the ousted Iraqi leader Saddam Hussein "produced and possessed chemical and biological weapons, and was trying to reconstitute his nuclear weapons programme."
However the BBC's Gordon Corera says the pair left many questions unanswered on the issue of intelligence and Iraq's weapons of mass destruction - an issue that has plagued both leaders domestically and which they hoped could be settled by developing a common line during the visit.
As to the fate of two UK nationals at Guantanamo Bay whose return Britain is seeking, Mr Bush said the issue would be discussed after the news conference. Mr Blair said a statement on the issue would be issued on Friday.
Mr Blair's speech to Congress took in a grand sweep of world affairs, from terrorism to peace in the Middle East to trade and sustainable development.
"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," Mr Blair said.
"But if our critics are wrong, if we are right as I believe with every fibre of instinct and conviction I have that we are, and we do not act, then we will have hesitated in face of this menace, when we should have given leadership. That is something history will not forgive," he said.
In the run-up to the war against Iraq, Mr Blair condemned the Iraqi human rights record, but stressed the legal basis of war was based on Iraq's failure to comply with UN resolutions on weapons of mass destruction.
However, the use of intelligence about Iraq's alleged weapons before the war - particularly about Iraq's nuclear ambitions - has put both leaders under fire.
The BBC's Laura Trevelyan says that even by admitting the possibility that he might have been wrong will give ammunition to Mr Blair's critics.
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".
He said Britain would stand by the United States.
"Our job is to be there with you - we will be with you in the fight for liberty," he said.
He dismissed the idea of creating a counterweight to American power as old fashioned.
But he called on the US to "listen as well as lead" in order to win hearts and minds around the world.
The US Congress had been expected during the visit to present Mr Blair with its highest civilian honour for his "steadfast" support of America "during a very trying and historic time for our two countries".
But the presentation of the Congressional Gold Medal has been postponed, reportedly because it has not yet been minted.
In his speech, Mr Blair also called for vigilance in the war against terrorism.
"The threat comes because, in another part of the globe, there is shadow and darkness where not all the world is free, where many millions suffer under brutal dictatorships, where a third of our planet lives in a poverty beyond anything even the poorest in our societies can imagine and where a fanatical strain of religious extremism has arisen that is a mutation of the true and peaceful faith of Islam," he said.
Other British leaders to address US Congress:
He 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.
Mr Bush later added to Mr Blair's comments on the Middle East, stating that it was essential for any Palestinian state to be built on "hope and reform, not violence".
He also linked the establishment of such a state with reform across the Middle Eastern region, not just within the Palestinian territories.
"The sooner terrorism is rooted out by all governments in the region the sooner a Palestinian flag will fly over a Palestinian state," he said.