Joe Biden has said the UK was fortunate to have had the Queen for 70 years, adding: “We all were, the world’s better for her.”
Mr Biden said it was an honour to meet the Queen and added that the late monarch reminded him of his mother.
Asked why the monarch reminded him of his mother, he said: “Just because of the way she touched when she leaned over. The way she had that look, like, ‘are you okay? Anything I can do for you? What do you need?’ and then also ‘make sure you do what you are supposed to do’.”
He said: “To all the people of England, all the people of the United Kingdom, our hearts go out to you and you were fortunate to have had her for 70 years.
“We all were. The world is better for her.”
Discussing the Queen’s impact on the wider world, Mr Biden said: “The American press has heard me say for a long time that I think the thing that is – maybe it’s too much if you excuse the expression, the Irish of it – it is about treating people with dignity.
“I talk about how my mother and father thought that everyone, no matter who they were, no matter what their station, no matter where they were from, deserved to be treated with dignity. And that’s exactly what she (the Queen) communicated, just the way she walked by, the way she acted.
“I think what she gave is a sense of maybe above all the notion of service. We all owe something. There’s something within our capacity to do that can make things, not just the world better, but your neighbourhood better, your household better, your workplace better. That’s what she communicated to me anyway and it was an honour to meet her.”
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Mr Biden continued: “Our hearts go out to the Royal Family. King Charles and all the family.
“It’s a loss that leaves a giant hole and sometimes you think you’ll never overcome it.
“But as I’ve told the King, she’s going to be with him every step of the way.”
Mr Biden and the first lady were joined by the US ambassador to the UK, Jane Hartley, when they arrived to see the Queen lying in state shortly before 5pm on Sunday.
They were greeted at Westminster Hall by Black Rod Sarah Clarke.
Large crowds were gathered behind barricades near Buckingham Palace and Parliament Square Garden ready to take photos of the motorcade.
Some children were sitting on their parents’ shoulders trying to get a view.
Security was tight and road crossings were closed ahead of the visit as rumours spread through the crowd about the imminent arrival of the president and his entourage.
Air Force One touched down at Stansted Airport just before 10pm on Saturday evening.
The president had been due to meet Prime Minister Liz Truss on Sunday but the talks were cancelled on Saturday.
A “full bilateral meeting” was scheduled for Wednesday when the leaders are set to be in New York for the UN General Assembly.
Meanwhile, the Princess of Wales held an audience with Ukraine’s first lady Olena Zelenska at Buckingham Palace.
The wife of Ukrainian President Volodymyr Zelenskyy had earlier visited Westminster Hall to see the Queen lying in state.
Ms Zelenska is in the UK to attend the state funeral while Mr Zelenksyy has remained in Ukraine as his troops fight Russian forces.