In a rare personal attack published hours after Washington announced tougher sanctions, the North Korean leader took aim at Trump over his maiden speech to the UN General Assembly in which he branded Kim "Rocket Man" and threatened to "totally destroy North Korea".
Trump "insulted me and my country in front of the eyes of the world and made the most ferocious declaration of a war in history", Kim said, according to the official Korean Central News Agency.
The dispatch was accompanied by a photo of the North Korean leader sitting behind a desk holding a piece of paper.
"I will surely and definitely tame the mentally deranged US dotard with fire," he said.
On the fringes of the UN General Assembly in New York, North Korean Foreign Minister Ri Yong-ho told reporters Pyongyang might now consider detonating a hydrogen bomb outside its territory.
"I think that it could be an H-bomb test at an unprecedented level perhaps over the Pacific," he said.
Trump's new executive order prohibits firms from operating in the United States if they deal with North Korea.
The move was the latest effort to tighten the screws on Pyongyang over its banned weapons programmes, following it sixth nuclear test -- the largest yet -- and the firing of two missiles over Japan in recent weeks.
It also came after the UN Security Council agreed a further set of sanctions on North Korea, aimed at reducing its ability to trade with the outside world.
Analysts say the sanctions show no signs of working, and cautioned that the increasingly ill-tempered and personal exchanges between Washington and Pyongyang did not augur well.
He added that Kim's rare first-person statement could also have been aimed at North Koreans.
"He is telling his country that the American president at the United Nations said he is going to totally destroy us... but I am not going to let that happen," Delury told AFP.
The statement was published today in North Korean newspapers and read out on state television by a star news anchor speaking over a still image of Kim at his desk.
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