Donald Trump proposed attacking North Korea with a nuclear weapon in meetings with aides and said that the US could blame the attack on another country, according to a book about his presidency.
Mr Trump is said to have made the remarks in 2017, his first year in office, when he was especially belligerent in his public comments about North Korea, warning Mr Kim in August of that year not to make any threats to the US as they would be "met with fire and fury like the world has never seen".
The following month, during his first address to the United Nations, Trump doubled down by telling the North Korean dictator that he would "totally destroy" his country and mockingly referring to him as "little rocket man".
White House officials, led by Mr Trump's recently appointed chief of staff John Kelly, were said to have been far more concerned that the president's discussions in private were similarly threatening.
Former Trump Organization executive Allen Weisselberg sentenced to five months in prison
One man's gaffe, another man's gift? What we know about the Biden classified documents discovery
Donald Trump sued over death of police officer after US Capitol riot
In an afterword due to be added to his 2020 book Donald Trump V. the United States, Michael Schmidt writes that Mr Trump had been threatening North Korea on social media in the days after Kelly took up the position.
In the new section of the book, due to be published next week, The New York Times' Washington correspondent adds: "What scared Kelly even more than the tweets was the fact that behind closed doors in the Oval Office, Trump continued to talk as if he wanted to go to war. He cavalierly discussed the idea of using a nuclear weapon against North Korea, saying that if he took such an action, the administration could blame someone else for it to absolve itself of responsibility."
Mr Schmidt also told Sky News' US partner NBC News that "behind closed doors in front of his aides, Trump would talk cavalierly about using force against North Korea, and there were deep concerns about this because Trump was saying things publicly that were signalling the potential of military conflict".
After Mr Trump suggested subterfuge to camouflage where the attack might come from, Kelly, a four-star general who many saw as a moderating force on the president during his 19-month tenure, pointed out that "it'd be tough to not have the finger pointed at us", according to the book.
Mr Trump continued to ratchet up the tension in 2018 on North Korea, tweeting to Kim Jong Un: "I have a Nuclear Button, but it is a much bigger & more powerful one than his, and my Button works!"
The following year, however, he became the first US president to meet his North Korean counterpart when the pair held a summit in Korea's demilitarised zone.