Kim lashed out after Trump stunned the world on Tuesday when he used his maiden UN General Assembly speech to warn the North that Washington would "totally destroy" it if the US or its allies were attacked.
The bellicose speech came after months of escalating tensions over advances in the rogue weapons programme operated by Pyongyang, which has defied tough sanctions to launch its sixth and largest nuclear test and to fire a series of missiles over Japan.
Kim, whom Trump belittles as "Rocket Man", also questioned the sanity of the US leader, referring to the "mentally deranged behavior of the US president openly expressing on the UN arena the unethical will to 'totally destroy' a sovereign state".
Isolated and impoverished, the North says it needs a nuclear deterrent to protect it from an aggressive US and the autocratic regime has made militarism a central part of its national ideology.
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Trump's remarks "have convinced me, rather than frightening or stopping me, that the path I chose is correct and that it is the one I have to follow to the last," Kim added.
The angry response also came after the US yesterday sharply ramped up sanctions aimed at curtailing North Korea's nuclear weapons drive, targeting the regime's trading partners with a sweeping ban on business.
Trump unveiled the new measures as he met with the leaders of allies Japan and South Korea, even as key players China and Russia voiced unease with his more aggressive approach.
The country also tested two intercontinental ballistic missiles in July that appeared to bring much of the US mainland into range.
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