SEOUL, South Korea — North Korea has long cultivated an image of defiant belligerence, punctuating its propaganda and diplomacy with colorful threats, insults and bluster. But by addressing President Trump in a personal statement on Friday, the nation’s leader, Kim Jong-un, has pushed his government’s brinkmanship to a new, potentially more perilous level.

In a statement written in the first person, published on the front pages of state newspapers and read on national television, Mr. Kim called Mr. Trump a “mentally deranged U.S. dotard” who had “denied the existence of and insulted me and my country in front of the eyes of the world.”

Mr. Kim vowed to take the “highest level of hard-line countermeasure in history.”

In a country where the leader is essentially portrayed as a god, Mr. Kim’s decision to respond personally to Mr. Trump’s speech to the United Nations General Assembly and pledge reprisals escalated the standoff over the North’s nuclear program in a way that neither he nor his predecessors had done before.

Though the statement made no mention of nuclear weapons, in the context of a political system built on a cult of personality, Mr. Kim’s intervention appeared to sharply reduce the possibility that his government might retreat or compromise, even in the face of war.