The Games in Pyeongchang next month have long been overshadowed by geopolitical tensions, with the North launching missiles capable of reaching the US mainland in recent months and detonating by far its most powerful nuclear device to date.
But Pyongyang - which boycotted the 1988 Summer Olympics in Seoul - yesterday agreed to send athletes and officials to the event as North and South held their first formal talks for two years at Panmunjom in the Demilitarised Zone (DMZ).
"Bringing North Korea to talks for denuclearisation is the next step we must take."
He was willing to hold a summit "at any time", he said, as long as it was "under the right conditions".
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"But it cannot be a meeting for meeting's sake. To hold a summit, the right conditions must be created and certain outcomes must be guaranteed."
Moon has long supported engagement with the North to bring it to the negotiating table over banned weapons programmes that have alarmed the US and the global community, and have seen Pyongyang subjected to multiple sets of United Nations sanctions.
"We have no difference in opinion with the US," Moon insisted, saying they shared an understanding about security, were working together and were both threatened by the North's nuclear weapons and missiles.
But he stressed that the aim of sanctions was to bring North Korea to talks, and "stronger sanctions and pressures could further heighten tensions and lead to accidental armed conflicts".
"But thankfully, North Korea came to dialogue before tensions were heightened further," he said.
Seoul had no plans to ease its own unilateral measures at present, Moon said.
"If I weren't involved, they wouldn't be talking about the Olympics right now, they'd be doing no talking," Trump said at the weekend, ahead of the meeting.
Moon thanked him for his efforts today. "I think President Trump's role in the realisation of inter-Korean talks was very big." he said. "I would like to express my gratitude."
The US cautiously welcomed the talks, but warned that the North's attendance at the Games should not undermine international efforts to isolate Kim's regime.
China - the North's major diplomatic backer and trade partner - and Russia, with which it also has strong ties, both welcomed the North-South talks.
And Japan's top government spokesman Yoshihide Suga said today that Tokyo "highly valued" Pyongyang's expressed willingness to participate in the Olympics.
"But there is no change in our policy of exerting the maximum level of pressure on North Korea until they change their policy, in close cooperation with the US, South Korea, and also involving China and Russia," he added.
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