The US president recalled the “kindness and hospitality” shown by the Queen, including when she hosted him and first lady Jill Biden in the UK, and said he wishes to continue a “close relationship” with the monarchy.
Charles and Mr Biden held a call ahead of the King marching behind his mother’s coffin before the lying in state in Westminster Hall.
The president said he spoke to Charles to “offer my condolences on the passing of Queen Elizabeth II”.
“I recalled her kindness, dignity, and constancy – and how she deepened the friendship between our nations. I also let the King know that I hope to continue a close relationship with him,” Mr Biden added.
A White House statement added that the president “fondly” remembered the Queen’s kindness and hospitality when she hosted the Bidens for tea at Windsor Castle after the G7 summit in Cornwall in June last year.
“He also conveyed the great admiration of the American people for the Queen, whose dignity and constancy deepened the enduring friendship and special relationship between the United States and the United Kingdom,” the White House added.
Mr Biden said he discussed Russian President Vladimir Putin and China’s Xi Jinping during his talks with the late monarch in Windsor.
After their meeting, he said: “We had a long talk. She was very generous. I don’t think she’d be insulted but she reminded me of my mother.
“In terms of the look of her and just the generosity. She was very gracious.”
From Republicans to Democrats, the Queen met 13 of the 14 US presidents during her 70-year reign, from Harry S Truman to Barack Obama and Donald Trump.