In a tweet on Wednesday, the US President responded to a speech made by the North Korea leader in which he said "a nuclear button is always on my desk".
Mr Trump wrote: "North Korean leader Kim Jong Un just stated that the 'nuclear button is on his desk at all times'.
"Will someone from his depleted and food starved regime please inform him that I too have a Nuclear Button, but it is a much bigger & more powerful one than his, and my Button works!"
The President's tweet - his 17th of the year so far - came hours after the US ambassador to the United Nations, Nikki Haley, warned Pyongyang against staging any further missile tests.
She told reporters on Tuesday that the US was hearing reports that the rogue state might be preparing another launch.
"I hope that doesn't happen. But if it does, we must bring even tougher measures to bear against the North Korean regime," she said.
Haley added that Washington would not take any talks between North and South Korea seriously if Mr Kim did not give up his nuclear weapons.
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