Tony Blair and George W Bush have reaffirmed the decisions they took over war in Iraq and said their countries would stay united against terrorism.
The British prime minister is on a final trip to Washington before stepping down at the end of June.
The two men - close allies for six years - praised each other's record.
Mr Bush called the British PM "a clear, strategic thinker". Mr Blair said the US president had been "unyielding, unflinching and determined".
Mr Blair insisted he would take the same decision again to stand "shoulder to shoulder" with America in the aftermath of the 11 September attacks.
He predicted that after he steps down and is succeeded by Gordon Brown, Britain would "remain a staunch and steadfast ally in the fight against terrorism in Iraq, and Afghanistan, and elsewhere".
Mr Bush said that when he had met Mr Brown recently he thought he was "a good fellow".
The president opened a good-humoured press conference with a joke at his own expense.
Mr Blair, he said, "is a good friend. He has led the British people for a long time, since 1797".
The deliberate slip echoed his mistake when introducing Britain's Queen Elizabeth II earlier this month, in which he said she had previously visited in 1776.
Mr Bush also offered to sing a Happy Birthday duet with Mr Blair to a reporter. She declined the offer.
The president said Mr Blair was "a good friend" and: "It has been a joy having you back here."
The president said the two men had held detailed talks on a number of issues, and held a video conference with commanders in Iraq.
He said both men were "frustrated at the inability of the international community to act with consequence in Darfur", and that they "spent a lot of time on climate change", which he described as "a serious issue".
The BBC's Matt Frei in Washington said the president ticked the boxes of topics that are important to Mr Blair, including Africa, climate change and Middle East peace.
However, there was no sign of him offering anything new in practical terms, our correspondent says.
Nevertheless, it was a heartfelt farewell by both men, he says.