The forthcoming summit would review the implementation of the inter-Korean summit agreement signed between the two countries during the first meeting in Panmunjom.
Kim said that his meeting with Moon would serve as a "historic chance" for the Korean people, who want to see the strengthening of inter-Korean relations.
The two leaders discussed the possible US-North Korea summit.
South Korean President's office says Kim promised to close N Korea's nuclear test site next month.
This is the third time that the two leaders are coming face to face, the last meeting being in May at Hanoi.
South Korea proposed that athletes from the two Koreas march together at the Games' opening ceremony and other joint activities between the two nations during the Winter Olympics.
After entering the Peace House for the inter-Korean summit, Kim wrote in the guest book 'a new history begins now'.
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'Much depends on Moon's persuasive skill to make both Trump and Kim shed some of their rigidity and be flexible to accommodate contrarian viewpoints,' says Dr Rajaram Panda.
'Hardliners who are against denuclearisation may be working secretly on North Korea's nuclear activities, despite official claims that dismantling its nuclear arsenal has already begun.'' 'Does it mean that Kim does not have full control over the military,' asks Dr Rajaram Panda.
Kim did not rule out diplomacy with the Biden administration despite that Pyongyang called Biden a 'rabid dog' after Biden labelled Kim a 'thug'.
The historic peace talks are aimed at ending their decades-long conflict and come weeks before Kim is due to meet United States President Donald Trump.
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The Korean summit, laden with symbolism in everything from the choice of location to the mango mousse for dessert, could just be the first round in a continuing dialogue, says Dr Rajaram Panda.
'Perhaps it isn't protocol at all, but power before which we abase ourselves,' says Sunanda K Datta-Ray.
'Xi Jinping is keen that the second Trump-Kim summit happens soonest.' 'Kim is reported to have told Xi that he expects to achieve a result from a second summit that the international community would welcome,' points out Dr Rajaram Panda.
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'Trump forgets that Kim is not one who likes to be treated publicly as a pauper; he wants to come to the table as an equal, and from a position of perceived strength, not as a suppliant,' says Dr Rajaram Panda.
'In the run-up to the summit, Trump had indicated that he might strike a nuclear deal in the course of a single meeting or over several days, but as it transpired, Trump departed Singapore soon after the meeting.' 'This raises questions if his aspirations for an ambitious outcome had been scaled back,' says Rajaram Panda.
'The coming two months could unfold unpredictable results or unpredictable consequences or both at the same time,' says Rajaram Panda.
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