Kim "made clear once again his intentions to completely denuclearize the Korean Peninsula", Moon said. North Korea's push to get the summit back on track shows that it's probably looking for sanctions relief, even as Kim retains concerns about his own security.
China, South Korea and the United States all back denuclearisation of the Korean Peninsula, but differ on how to make that happen.
Kim reaffirmed his commitment to "complete" denuclearization of the Korean Peninsula and to a planned meeting with Trump, Moon told a news conference in Seoul.
Following an unusually provocative 2017 in which Kim's engineers tested a purported thermonuclear warhead and three long-range missiles theoretically capable of striking mainland USA cities, the North Korean leader has engaged in a flurry of diplomatic activity in recent months.
Moon suggested that "it is necessary for the two sides to engage in direct talks to eliminate misunderstandings and have sufficient preliminary, working level negotiations concerning the agenda".
She also said it was up to the Americans whether they would "meet us at a meeting room or encounter us at nuclear-to-nuclear showdown".
President Moon maintained that Kim is committed to "complete" denuclearization, but acknowledged that Pyongyang and Washington may have differing expectations of what denuclearization means.
The two Koreas planned to hold a meeting last week, but the North called if off at the last minute, taking issue with joint military drills between South Korea and the United States.
China has been angling to retain its influence over North Korea amid the recent rapprochement between the two Koreas. The summit―preceded by multiple meetings with South Korean president Moon Jae-in―was set up to discuss the prospect of denuclearization among other contentious topics.
The developments, after last week's whirlwind of uncertainty, appeared to flesh out Trump's assertion that the June 12 summit in Singapore that he canceled Thursday could take place as first scheduled. "If you change your mind having to do with this most important summit, please do not hesitate to call me or write".
Sung Kim, a former US ambassador to South Korea and former nuclear negotiator with the North, has been called in from his posting as envoy to the Philippines to lead the preparations, according to a person familiar with the arrangements. That's according to his South Korean negotiating partner, President Moon Jae-in, who met on Kim's request. Allison Hooker, a Korea specialist on the National Security Council, is reportedly also part of the team.
In previous, failed talks, North Korea said it could consider giving up its arsenal if Washington removed its troops from South Korea and withdrew its so-called nuclear umbrella of deterrence from South Korea and Japan.
"In Trump's thinking, his "maximum pressure" would've resulted in Kim kneeling and returning to dialogue in surrender anyway if it reached the boiling point", he said.
Mr. Moon is the only South Korean leader to have met a North Korean leader twice, both times in the DMZ, which is a symbol of the unending hostilities between the nations after the Korean War ended in 1953 in a truce, not a peace treaty.