In the statement released Thursday, Kim also said North Korea is considering the strongest possible response to what he called Trump's provocation.
"I'd like to advise Trump to exercise prudence in selecting words and to be considerate of whom he speaks to when making a speech in front of the world," Kim said, according to The Associated Press.
Trump responded to Kim's threats on Twitter Friday morning, saying he "would be tested like never before."
North Korea Foreign Minister Ri Yong-ho, who is in New York for the UN General Assembly, said Thursday evening that North Korea could detonate an H-bomb over the Pacific Ocean, but also told reporters, "we have no idea about what actions could be taken as it will be ordered by leader Kim Jong Un."
On Tuesday, Trump threatened to "totally destroy" North Korea, referring to Kim as "Rocket Man."
"No nation on earth has an interest in seeing this band of criminals arm itself with nuclear weapons and missiles," Trump said. "The United States has great strength and patience, but if it is forced to defend itself or its allies, we will have no choice but to totally destroy North Korea. Rocket Man is on a suicide mission for himself and for his regime. The United States is ready, willing and able, but hopefully this will not be necessary."
Trump also called on all nations to isolate the Kim regime in light of its "reckless pursuit" of nuclear weapons and treatment of its citizens.
In his lengthy response, Kim slammed Trump as "mentally deranged" and said the American president had "made the most ferocious declaration of a war in history."
"I will make the man holding the prerogative of the supreme command in the U.S. pay dearly for his speech calling for totally destroying" North Korea, Kim said.
Kim added: "Whatever Trump might have expected, he will face results beyond his expectation.
"I will surely and definitely tame the mentally deranged U. S. dotard with fire."