The King has sent a personal message of congratulations to Donald Trump on his inauguration, reflecting on the enduring special relationship between the UK and US, Buckingham Palace said.
Charles’s private written words were delivered to mark Mr Trump being sworn into office as US president for a second time.
It is understood all options remain possible for an incoming state visit visit by Mr Trump to the UK and a visit by Charles to the US, but no plans are currently in the diary.
Foreign monarchs, presidents or prime ministers are invited to visit the King on the advice and request of the Foreign and Commonwealth Office, with the decision down to the Government.
With the Republican politician making the most dramatic comeback in US political history, Charles and Mr Trump will be expected to encounter one another face to face once again during Trump 2.0, as his second term in office is being dubbed.
Mr Trump is well known for his love of the monarchy and the royal family plays a central role in the UK’s bond with the US.
The US leader boasted he had “automatic chemistry” with the late Queen, and has hailed the King as a “really wonderful guy”.
When Mr Trump met the Prince of Wales in Paris last month after the ceremonial reopening of the Notre Dame cathedral, he remarked of William that he was “very handsome” and “some people look better in person”.
Sir Keir Starmer is set to hold talks with Mr Trump in Washington within weeks as the “special relationship” faces strain, with high-profile Labour figures having expressed critical opinions about Mr Trump in the past.
Mr Trump is weighing up whether to approve the appointment of Lord Mandelson as the UK’s new ambassador in Washington, the fate of the Chagos Islands deal and the extent to which tariffs will hit Britain.
He was already feted with a grand state visit to the UK, hosted by the Queen in 2019.
Precedent for second-term US presidents who have already made a state visit is usually tea or lunch with the monarch at Windsor Castle, as was the case for George W Bush and Barack Obama.
But nothing should be ruled out when it comes to Mr Trump, who is first ever US president to be a convicted felon in the wake of his New York hush money trial.
His election victory marked an extraordinary comeback in a political career which has been marred in controversy, criminal charges, accusations of racism and sexism, and the US Capitol riots in January 2021.
The last outward state visit to the US by a British monarch was 17 years ago when Elizabeth II was hosted by George W Bush in 2007.
The King and Queen could be invited to the US by Mr Trump.
Palace officials indicated that after Charles and Camilla’s recent Australia tour that the King will return to regular overseas trips this year as he adapts to living with cancer.
Mr Trump has often spoken of his bond with Elizabeth II, saying: “I really got to know her because I sat with her many times and we had automatic chemistry, you will understand that feeling.”
But author Craig Brown, in his biography A Voyage Around The Queen, has since claimed that the monarch found Mr Trump “very rude”.
She is said to have “particularly disliked” the way he “couldn’t stop looking over her shoulder, as though in search of others more interesting”.
In 2018, Mr Trump joined the Queen for tea at Windsor Castle.
As they inspected a Guard of Honour, the president walked along before standing still in front of the Queen, meaning she had to navigate her way around him so they could walk side by side.
He later said of the sovereign: “That is a beautiful woman.”
At the state visit a year later, he was treated to a full programme of pomp and pageantry, with a ceremonial welcome and a glittering ballroom banquet at Buckingham Palace.
Charles inspected a Guard of Honour with Mr Trump on the lawns of the royal residence, dined with him at the banquet and had tea with him, Mrs Trump and the then-Duchess of Cornwall at Clarence House.
The returning-First Lady Melania Trump wrote in her memoir that she and her husband have an ongoing letter correspondence with the monarch.
Mr Trump has admitted, however, that the King is “a little bit more into environmental restriction than I am”.
While Charles, known for his eco-credentials, has warned climate change is “the wolf at the door”, Mr Trump has branded it a “Chinese hoax”.
But Mr Trump maintained he “totally listened” to the then-prince when he was pressed on climate change by Charles during his 2019 visit.
The King wrote privately to Mr Trump after he survived an assassination attempt, condemning the violence and wishing him a quick recovery.
The now-47th American president has, however, been publicly critical of the Duke and Duchess of Sussex, who live in the US with their children, and warned Harry could face consequences if he lied about taking drugs on his US visa application.
He also lambasted the duke and Meghan, accusing them of treating the late Queen “very disrespectfully”.
Mr Trump also used to bombard Diana, Princess of Wales, William and Harry’s late mother, at Kensington Palace with massive bouquets, according to broadcaster Selina Scott, who said he saw the princess as “the ultimate trophy wife”.