The president also signed the book of condolence at Lancaster House before a reception at Buckingham Palace tonight.
He was 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.
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The King and Queen Consort are set to host world leaders and official overseas guests at the palace in an “official state event” later today.
Biden will be just one of 500 heads of state and VIPs at the Queen’s funeral on Monday.
He will be joined by fellow G7 leaders French President Emmanuel Macron, German President Frank-Walter Steinmeier, Italian President Sergio Mattarella, Canadian PM Justin Trudeau and Japanese Emperor Naruhito.
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Other royals attending include the kings of Belgium, Bhutan, Jordan, Lesotho, the Netherlands, Norway, Saudi Arabia, Spain, Sweden, and Tonga.
The Queen of Denmark will be there, too, alongside the crown princes of Bahrain, Kuwait and Liechtenstein, plus the sultans of Brunei and Oman.
New Zealand will be represented by Maori King Tuheitia Paki and PM Jacinda Ardern.
Other Commonwealth leaders include Australian PM Anthony Albanese, South African President Cyril Ramaphosa, Indian President Droupadi Murmu and Jamaican PM Andrew Holness.
European Commission President Ursula von der Leyen and European Council President Charles Michel will both attend, as will Ukrainian first lady Olena Zelenska, Irish President Michael D Higgins and Taoiseach Micheál Martin.
China’s Vice-President Wang Qishan, Brazil’s President Jair Bolsonaro and South Korean President Yoon Suk-yeol are all invited.
But six countries — Russia, Belarus, Myanmar, Afghanistan, Syria and Venezuela — were overlooked when the funeral invitations were sent out.
Two million mourners are set to descend on London on Monday.
And at 8pm tonight the country will observe a minute's silence to remember the Queen.
People have been invited to mark the occasion privately at home, on their doorstep or street, or at community events and vigils.
It will come shortly after the Queen Consort pays a televised tribute to the late monarch, recalling her “wonderful blue eyes” and saying: “I will always remember her smile.”
Camilla, in pre-recorded words on the BBC, will speak of how Queen Elizabeth II was a “solitary woman” in a male-dominated world.
She will add: “I can’t remember anyone except the Queen being there.”
There will also be a service of reflection near Falkirk, Scotland at 7.30pm.
It will see 96 lanterns, one for each year of the late monarch’s life, lowered into the pool of reflection at the foot of the Queen Elizabeth II Canal, before wreaths are placed into the water.
It comes after King Charles held an audience with Ms Truss this afternoon.
His Majesty was pictured laughing with the Prime Minister after she shook his hand and curtseyed to him this afternoon.
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It is Ms Truss' third audience with the King since he became monarch earlier this month.
The PM will also meet Irish Taoiseach Micheal Martin, Canadian prime minister Justin Trudeau and Polish president Andrzej Duda in Downing Street.