President Biden became the 13th US head of state to be received by Britain's Queen Elizabeth II, who welcomed him and First Lady Jill Biden to Windsor Castle on Sunday.
The visit included a Guard of Honour and afternoon tea with the monarch.
Reporters were not allowed in the castle for the talks, though they heard the queen and the president engaged in polite conversation as they walked into Windsor.
The first lady spent time with the Queen's granddaughter-in-law, attending a school with her in Cornwall on Friday, where the pair met some of the pupils in reception class, before sitting on a round table about education and Early Years development. However, it appears that the faux pas by the USA president didn't affect the meeting as the monarch seemed happy when she greeted Joe Biden and First Lady Jill.
They were greeted by the Queen at the dais in the castle's quadrangle.
The trio enjoyed a Guard of Honour formed of The Queen's Company First Battalion Grenadier Guards, and the USA national anthem was played beneath blue skies and hot sunshine.
The queen has hosted four other American presidents at Windsor Castle in recent years, including former-President Donald Trump in 2018, who shocked press and palace pundits when he breached royal protocol by walking ahead of the queen, at times blocking her view and giving her his back. Prince Philip, Duke of Edinburgh, died in April.
After leaving Windsor, Biden will head off to a North Atlantic Treaty Organisation summit in Brussels on Monday, a U.S. -EU summit on Tuesday and a meeting with Russian President Vladimir Putin in Geneva the following day.
As he was leaving the UK, Biden told waiting reporters about the visit: "We had a long talk".
"I wish her all the very best".
Afterward, he described her as an "extremely gracious" woman who reminded him of the mother who offered him that advice 40 years ago.
It came just hours after she had returned to Windsor from Cornwall, where she met G7 leaders and posed for the traditional "family photo", prompting chuckles as she quipped: "Are you supposed to look as if you're enjoying yourself?"
He said he had invited her to the White House, and that he joked the presidential home and office could fit inside the Quadrangle of her Berkshire castle.
One of the major parts of the queen's official birthday is her award of honors to those deemed to have made a positive contribution to society.
It was the second consecutive year that her official birthday was marked at Windsor Castle, rather than on Horse Guards, due to the pandemic. Sunday's high-profile reception for the Bidens, which included a military band playing both the British and U.S. national anthems, means she has now formally met 13 of the last 14 sitting USA presidents - barring During her 69 years on the throne, there have been 14 USA presidents.
During her 69 years on the throne, there have been 14 USA presidents.