"The United States can never fight a war against me and our state," he said in the nationally televised speech. "It should properly know that the whole territory of the U.S. is within the range of our nuclear strike and a nuclear button is always on the desk of my office, and this is just a reality, not a threat."
But Kim also said that North Korea was a peace-loving and responsible nuclear power, and would not use its nuclear weapons unless "hostile aggression forces" encroach on its sovereignty or interests.
"This year, we should focus on mass-producing nuclear warheads and ballistic missiles for operational deployment," Kim said. "These weapons will be used only if our security is threatened."
North Korea conducted its sixth and most powerful nuclear test in September and launched its most high-tech intercontinental ballistic missile in November, ignoring international condemnation and steadily tightening sanctions.
In typically bellicose language, it declared the latest round of United Nations sanctions imposed last month an "act of war," and Kim said his country had achieved the historic feat of "completing" its nuclear forces.
North Korea's nuclear capabilities do not yet match Kim's boasts, experts say, since it is far from clear it could successfully deliver a nuclear weapon on one of its missiles. Yet there is little doubt its capabilities have advanced significantly in the past year.
But Kim, dressed in a Western-style gray suit and tie, also offered a potential olive branch to Seoul, saying it is imperative to lower military tensions on the Korean Peninsula and improve ties with the South.
He said that the path to dialogue was open and that he would consider sending a delegation to the Winter Olympics in Pyeongchang, South Korea.
"North Korea's participation in the Winter Games will be a good opportunity to show unity of the people, and we wish the Games will be a success," he said. "Officials from the two Koreas may urgently meet to discuss the possibility."
South Korea has been trying to reassure the rest of the world that the Olympics will be safe despite the nuclear tensions, and President Moon Jae-in has said North Korea's participation would ensure their safety. He also proposed last month that Seoul and Washington postpone annual joint military drills until after the Olympics, and he generally takes a less-confrontational approach to relations with the North than his predecessor, Park Geun-hye.
John Delury, a professor of international relations at Yonsei University in Seoul, said Kim's message to Seoul was "more promising" than he had anticipated, addressing in a specific and actionable way South Korea's desire to make the Games a success.
"That should give hope to those in the South who are trying to get something going and open a channel at least," he said.
The idea of improving relations between the two Koreas is one that is frequently spoken about but seldom achieved, and Kim's warmer words could also be seen as an attempt to drive a wedge between Seoul and Washington.
While Kim's words were more combative toward the United States, he also refrained from a personal attack on President Trump, after the two men engaged in several rounds of mutual name-calling in 2017, Delury noted.
When asked about North Korea's nuclear claims Sunday night, Trump said only, "We'll see, we'll see."
Daryl Kimball, executive director of the Arms Control Association, said Kim's claims about his country's nuclear capability underscored that there was no viable "military solution" to denuclearizing North Korea and that sanctions alone would not persuade Pyongyang to halt or reverse its nuclear buildup.
"To avoid a nuclear conflict and the full-scale deployment of an operational North Korean strategic deterrent force, U.S. leaders, in concert with South Korea, should redouble efforts to engage North Korea in direct talks and cease any further explicit or implicit threats of military action against the North," he said in an email.
"The upcoming Olympics provide an important opportunity to break the ice and to begin discussions with the North Koreans on mutual steps that reduce the chances of miscalculation and war," he added.