Trump and Kim get into verbal fight calling each other mad.
North Korea and US have engaged in ever more heated rhetoric in recent months.
North Korea's chief Kim Jong-un has said remarks by "deranged" US President Donald Trump have convinced him he is right to develop weapons for North Korea.
In an unprecedented personal statement Kim said Trump would "pay dearly" for a UN speech where he threatened to "totally destroy" the North if the US was forced to defend itself.
Trump replied that the "madman... will be tested like never before". Kim ended his statement by saying he would "surely and definitely tame the mentally deranged US dotard with fire"
North Korean Foreign Minister Ri Yong-ho, who had earlier compared Mr Trump's speech to "the sound of a barking dog" has warned that Pyongyang could test a hydrogen bomb in the Pacific Ocean in response to the US president's threat.
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