Donald Trump was unaware the UK was a nuclear power, according to a book by his former national security adviser John Bolton.
The US President is alleged to have made the comments about British military capability at a meeting with former PM Theresa May two years ago.
Mr Bolton, who worked in the White House for 17 months, said the president was "stunningly uninformed".
Foreign Secretary Dominic Raab declined to comment on the claim on Thursday.
Mr Bolton's 577-page tome, The Room Where It Happened, is due to go on sale next week - but the Trump administration is trying to block its publication.
In a tweet, the president described the book as "made up of lies and fake stories".
According to one excerpt, the UK's nuclear arsenal came up during a meeting with Mrs May in 2018, when it was mentioned by one of the then-prime minister's officials.
According to the book, Mr Trump said: "Oh, are you a nuclear power?" Mr Bolton said he could tell it "was not intended as a joke".
Mr Bolton left the White House in September 2019, saying he had quit as national security adviser. Mr Trump however said he had fired Mr Bolton because he disagreed "strongly" with him.
Nine countries currently have nuclear weapons: the US, UK, Russia, France, China, India, Pakistan, Israel and North Korea.
UK nuclear history
The UK developed and tested its own nuclear weapons in the early 1950s, at a time when the US government did not share the technology with its wartime ally.
The UK's nuclear bombs were initially carried by the RAF's V-force but the government later purchased the submarine-based Polaris missile system from the US, which became one of the cornerstones of NATO's cold war defences.
The current submarine-based system - known as Trident - was launched in the 1990s, after Margaret Thatcher decided to replace Polaris in 1980.
It is named after the Trident missiles they carry, which are serviced at a port in the US. Some warhead components are also made in America.
British governments have always stressed Trident's independence, saying its firing does not require the permission, the satellites or the codes of the US.
But critics argue the UK is technically so dependent on the US that in effect Trident is not an independent system.
Asked about the reports of the book on Thursday, Mr Raab said he did not want to get "dragged into the commentary" on its publication.
"Trying to get me to comment on books from a former member of the administration is not my focus," he told BBC Radio 4's Today programme.
"I don't know the answer to it," he added.