Kim used his annual New Year address to underscore Pyongyang's claim that it has developed a weapons deterrent and warn that he had a "nuclear button" on hand, but sweetened his remarks by expressing an interest in dialogue and participating in the South's Games.
South Korea's unification minister Cho Myoung-Gyon said Seoul was "reiterating our willingness to hold talks with the North at any time and place in any form".
"We hope that the South and North can sit face to face and discuss the participation of the North Korean delegation at the Pyeongchang Games as well as other issues of mutual interest for the improvement of inter-Korean ties," he said at a press conference.
The two Koreas, which have been separated by a tense demilitarised zone since the end of the 1950-53 Korean war, last held high-level talks in 2015.
Dovish South Korean President Moon Jae-In, who has long favoured engagement to defuse tension with the North, earlier Tuesday welcomed Kim's suggestion that there could be an opportunity to kick-start dialogue.
However, he indicated that improvements in inter-Korean ties must go hand in hand with steps towards denuclearisation.
Moon proposed Red Cross and military talks last year, but his requests were not answered by Pyongyang.
The North has rattled the international community in recent months with multiple missile launches and its sixth and most powerful nuclear test -- purportedly of a hydrogen bomb.
Pyongyang has shrugged off a raft of new sanctions and heightened rhetoric from the United States as it continued to drive forwards with a weapons programme that it says is defensive and aimed at developing a warhead capable of targeting the US mainland.
Kim's comments were the first indication of North Korea's willingness to participate in the Winter Games, which run from February 9 to 25.
Moon called them a "positive response" to Seoul's hope that the Pyeongchang Olympics would be a "groundbreaking opportunity for peace".
The main Winter Olympic venues are just 80 kilometres (50 miles) from the heavily fortified border with the North and the build-up to the event has been overshadowed by surging tensions over Pyongyang's nuclear and missile tests.
In his speech Monday, Kim said the Olympics could provide a reason for officials from the neighbours "to meet in the near future".
Seoul and the Games organisers are keen for the North to take part.
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