Ri Yong-ho told the General Assembly that Trump's vow to "totally destroy" his country had made "our rockets' visit to the entire US mainland all the more inevitable."
Describing Trump as a "mentally deranged person full of megalomania," Ri said the US leader who "holds the nuclear button" posed "the gravest threat to international peace and security today."
In his first address to the General Assembly, Trump called leader Kim Jong-Un "Rocket Man" on a "suicide mission," prompting Kim to warn in turn that the US president would "pay dearly" for his threat.
North Korea in recent weeks detonated its sixth nuclear bomb and has test-fired intercontinental missiles -- saying it needs to defend itself against hostility from the United States and its allies.
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The United States led a push at the United Nations for tough sanctions that were adopted on September 11, and has imposed unilateral measures to punish firms that do business with North Korea.
Calling the resolutions unjustified, Ri said that Pyongyang was left with no other choice but to respond with the "nuclear hammer of justice."
The Pentagon said the mission was a "demonstration of US resolve and a clear message that the president has many military options to defeat any threat.