"And depending on their outcomes, they may lead to a three-way summit of South, North and U.S.", Moon said at the presidential Blue House in Seoul, quoted by the Yonhap news agency.
Finally, when Chuang Eui-yong, the South Korean Nation Security Adviser, led a South Korean delegation to North Korea, Kim and his senior members expressed the desire to hold talks with the United States with regard to denuclearization and improving ties with the US.
Kim told visiting South Korean officials that he would meet with Moon in late April as the rival nations moved to improve relations amid rising tensions over the North's nuclear weapons program.
The talks were first proposed by South Korea to be held in the Panmunjom truce village in the Korean Demilitarized Zone.
A team of three officials will be led by Ri Son Gwon, the chairman of North Korea's committee for the peaceful reunification of the country, the South's Unification Ministry said.
Some 18 delegates from the three countries, including Choe Kang Il, a deputy director general for North American affairs at North Korea's foreign ministry, came to Finland earlier this week for a "track 2" conference amid a series of diplomatic encounters ahead of a possible US-North Korean summit.More news: March Madness Sweet 16 has unexpected field after NCAA Tournament favorites ousted
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The inter-Korean summit is due to be followed by a face-to-face meeting between US President Donald Trump and Kim by the end of May. But there had been no official word from Pyongyang.
-North Korea talks would be what nuclear disarmament steps Kim would promise in return for what concessions from the United States and whether Trump would accept them.
Among the six North Korean delegates was senior diplomat Choe Kang Il, who handles North American affairs for his government, while the US delegation is believed to have included Kathleen Stephens, the former USA ambassador to South Korea.
The team used a plane belonging to North Korea's Air Koryo, North Korea's sole airline, which is on the blacklist of USA sanctions.
The lack of North Korean confirmation that Kim was willing to meet Trump to talk about denuclearization has only exacerbated those doubts.
In a surprising turn of events linked to the Winter Olympics, held in South Korea in February, North Korea first invited South Korean President Moon Jae-in to a summit with Kim, planned for late next month in the demilitarized zone that divides the Korean Peninsula.