Vice-president Dick Cheney and secretary of state Condoleezza Rice were among the guests at the five-course reception in the White House's state dining room attended by 134 guests, said to be a "diverse representation… from across the country".
"We're confident that Anglo-American friendship will endure for centuries to come," President Bush said.
The Queen also reflected upon the relationship between wartime leaders Winston Churchill and Franklin Roosevelt as a gleaming example of international relations.
"I grew up in the knowledge that the very survival of Britain was bound up in that vital wartime alliance forged by Winston Churchill and President Roosevelt," the Queen told the reception.
"Whether in Iraq or Afghanistan, climate change or the eradication of poverty, the international community is grappling with problems certainly no less complex than those faced by our 20th century forebears."
Referring to problems of international terrorism the Queen added: "Together with our friends in Europe and beyond we can continue to learn from the inspiration and vision of those earlier statesmen in ensuring that we meet these threats and resolve these problems."
The royal tour began in Virginia last week as the Queen and Prince Philip visited Richmond, Williamsburg and Jamestown to mark the 400th anniversary of the Jamestown settlement.
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