However, Kim's foreign minister, Ri Yong Ho, said in televised remarks North Korea could consider a hydrogen bomb test of an unprecedented scale over the Pacific Ocean.
Ri, who was talking to reporters in New York ahead of a planned address later this week, also said he did not know Kim's exact thoughts.
Japan, the only country ever to suffer an atomic attack, described the threat as "totally unacceptable".
Trump said in his first address to the United Nations on Tuesday he would "totally destroy" North Korea, a country of 26 million people, if it threatened the United States and its allies, and called Kim a "rocket man" on a suicide mission.
Kim said the North would consider the "highest level of hard-line countermeasure in history" against the United States and that Trump's comments had confirmed his own nuclear program was "the correct path".
Pyongyang conducted its sixth and largest nuclear test on Sept. 3 and has launched dozens of missiles this year as it accelerates a program aimed at enabling it to target the United States with a nuclear-tipped missile.
"I will surely and definitely tame the mentally deranged U.S. dotard with fire," Kim said in the statement carried by the KCNA state news agency.
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