The comments follow months of fiery rhetoric between the two countries that have seen tensions soar, with Trump drawing criticism at home for repeatedly using highly-menacing language towards the reclusive state.
During Wednesday's address, he criticised the "cruel dictatorship" of Kim Jong-Un and the leader's "reckless pursuit" of atomic weapons while vowing to wage "a campaign of maximum pressure" to derail the nuclear threat.
Kim declared his country a fully-fledged nuclear power last November after testing an intercontinental ballistic missile Pyongyang claimed is capable of reaching the US mainland.
Trump also lashed out at widespread human rights abuses under the regime and highlighted the case of Otto Warmbier, an American student who died last year shortly after being released from a 17-month-long detention in North Korea.
A spokesperson of the North's foreign ministry on Sunday said the speech reflected "the height of Trump-style arrogance, arbitrariness and self-conceit," in a statement carried by the state-run KCNA news agency.
"Trump also insisted upon the 'maximum pressure' against our country, viciously slandering our most superior people-centered social system," the statement added.
"However, it is no less than screams of Trump terrified at the power of the DPRK that has achieved the great historic cause of completing the state nuclear force and rapidly emerged as the strategic state recognized by the world," it said, using the North's official name.
Also in his address, Trump honoured Ji Seong-Ho, a North Korean defector with only one arm and one leg who made a dramatic, 6,000-mile journey to the South after suffering severe discrimination and torture at home.
The North claimed Trump's comment revealed a "sinister intention to do something against us by relying on strength while talking about 'American resolve.'"
"If Trump does not get rid of his anachronistic and dogmatic way of thinking, it will only bring about the consequence of further endangering security and future of the United States," the foreign ministry said.
Relations between the two countries reached fresh lows last year with the North launching a series of missiles and staging its most powerful nuclear test to date, in a challenge to Trump who has threatened to "utterly destroy" the regime in the event of an attack.
Kim and Trump have at the same time traded colourful personal barbs against each other, sparking global alarm and fears of further fighting on the peninsula that was left in ruins after the 1950-53 Korean War.
But in a move that seemed aimed at easing tensions and after months of persuasion from Seoul, the North last month said it would send its athletes to the Winter Olympics, due to kick off in the South on Friday.
Some have already arrived in South Korea.
Analysts have described the potential momentum for peace as too fragile, saying it may not be sustainable after the Games given the North's repeated declarations of nuclear statehood.
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