"The United States should know that the button for nuclear weapons is on my table", he said during the nationally televised speech, according to a provisional translation by The Associated Press.
South Korean Unification Minister Cho Myong-gyon offered on Tuesday high-ranking government talks with North Korea next week at the border village of Panmunjom, a day after Pyongyang suggested talks despite sticking to its nuclear ambitions.
He continued that theme in his New Year's address, announcing that North Korea would focus in the coming year on "mass producing nuclear warheads and ballistic missiles for operational deployment".
Rather than encouraging US measures that "threaten the security and peace of the Korean peninsula", Seoul should instead respond to overtures from the North, and "stop nuclear war exercises with foreign forces", Kim said.
North Korea, which regularly threatens to destroy the United States, South Korea and Japan, tested its most powerful intercontinental ballistic missile in November, which it said was capable of delivering a warhead to anywhere in the United States.
Games organisers and Seoul have both been keen for the North to take part, but Pyongyang's participation in sporting events in the South has largely depended on the political and military situation on the Korean peninsula.
Cho told a media conference he expects the two Koreas to focus on bringing a North Korean delegation to the Pyeongchang Winter Olympics, which begin next month, should the talks be held on January 9. "Officials from the two Koreas may urgently meet to discuss the possibility", Kim said.
Kim says North Korea could participate in South's Winter Olympics
South Korean President Moon Jae In has said North Korea's participation will ensure safety of the Pyeongchang Olympics and proposed last month that Seoul and Washington postpone large military drills that the North denounces as a rehearsal for war until after the Games. While Kim did not halt his nuclear threats, the fact that he hinted at his willingness to improve inter-Korean relations by having North Koreans attend the Pyeongchang Winter Olympics was a positive sign.
Kim's hostile comments were offset by a diplomatic message.
In the speech, Kim also stressed North Korea's economic achievements and noted the importance of improving the nation's standard of living, the AP reported.
"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. However, he also steadfastly declared North Korea a nuclear power.
"It is quite noteworthy that the North's leader himself says the North is willing to participate in Pyeongchang", Professor Yang Moo-Jin of the University of North Korean Studies in Seoul told AFP.
"An improvement in inter-Korean relations may not go a separate way from (efforts) to resolve the North Korean nuclear issue, so I ask the foreign ministry to closely consult with our allies and the global community so that we may push for an improvement in inter-Korean relationship and the resolution of the North Korean nuclear issue at the same time", he said. "Without launching missiles and conducting a nuclear test, North Korea will be in the spotlight just by attending the Winter Olympics".
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