The country's state-run media criticised the President's claim that he has a "much bigger and more powerful" nuclear button than Kim Jong Un.
Mr Trump had taken aim at North Korea's nuclear ambitions in a January 3 tweet.
"North Korean Leader Kim Jong Un just stated that the "Nuclear Button is on his desk at all times." he wrote.
"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!"
North Korea's ruling party newspaper, Rodong Sinmun, responded to the comments in a commentary on Tuesday.
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