It is unusual for the North Korean leader to issue such a statement in his own name.
Asian stocks fell and the Japanese yen and Swiss franc gained on the possibility of a hydrogen bomb test in the Pacific.
North Korean leader Kim Jong Un called Mr Donald Trump a "dotard" and threatened to take the most "hardline countermeasure in history" after the US President warned that America, if threatened, would "totally destroy" the "rocket man" and his communist state.
On Tuesday, during what was his first appearance before the UN General Assembly, Trump said Kim was "on a suicide mission" and asserted that if North Korea continued its provocations, the United States would "have no choice but to totally destroy" the country.
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But the North Korean leader said remarks by the "deranged" US President convinced him he is right to develop weapons for North Korea.
"North Korea has retaliated by escalating its nuclear testing including a possibility of a hydrogen bomb". North Korea has launched in what it says are tests of several missiles, some of which are believed to be able to strike the United States.
Kim said Trump's comments were reflective of "mentally deranged behavior". "Whatever Trump might have expected, he will face results beyond his expectation".
North Korea has created problems with its allies.
North Korea has continued making threats after the sanctions. The Rodong Sinmun printed Friday a photo of Kim reading the statement from the Workers' Party's Central Committee building on its front page.
Pierce took to Twitter to agree with Kim's statement.
Lavrov said Russian Federation was working with other countries "to strive for the reasonable and not the emotional approach - instead of the kindergarden fight between children (where) no one can stop them".
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