Usually, correspondence written by the King is not made public, but Donald Trump held up the letter in the Oval Office.
Here is what we are able to make out from photos.
In the opening paragraph, the King references the “breadth of challenges across the world”, and says the UK and the US have “a vital role to play”.
Follow live: Trump questioned about Zelenskyy ‘dictator’ comment

Pic: Reuters
He goes on to say that he remembers “with great fondness” Mr Trump’s visits to the UK during his “previous presidency”.
The King mentions Mr Trump visiting his golf course in Turnberry and then appears to suggest a visit Balmoral or Dumfries House in Scotland at some stage – estates owned or run by the monarch.
He writes: “There is much on both Estates which I think you might find interesting and enjoy – particularly as my Foundation at Dumfries House provides hospitality skills-training for young people who often end up as staff in your own establishments!
“Quite apart from this presenting an opportunity to discuss a wide range of issues of mutual interest, it would also offer a valuable chance to plan a historic second State Visit to the United Kingdom.
“As you will know, this is unprecedented by a US president. That is why I would find it helpful for us to be able to discuss, together, a range of options for location and programme content.
“In so doing, working together, I know we will further enhance the special relationship between our two countries, of which we are both so proud.”
Sky News has contacted Buckingham Palace to ask when the second state visit might take place, and they said: “When diaries allow.”
This breaking news story is being updated and more details will be published shortly.
Please refresh the page for the fullest version.
You can receive breaking news alerts on a smartphone or tablet via the Sky News app. You can also follow us on WhatsApp and subscribe to our YouTube channel to keep up with the latest news.