"We need to continue efforts to hold a peace Olympics," Moon told a press conference. "We need to peacefully resolve North Korea's nuclear issue."
Delegates from North and South Korea held their first official talks for two years yesterday at Panmunjom in the Demilitarized Zone that has divided the peninsula for decades.
Pyongyang boycotted the 1988 Summer Olympics in Seoul, but they agreed that this time the North would send athletes and officials to the Games, which begin in Pyeongchang next month.
The North's leader Kim Jong-Un and US President Donald Trump have traded personal insults and threats of war.
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But Moon said: "I will clear away the anxiety and distrust that have become deeply rooted in the lives of the people.
"Step by step, together with the people, I will create a peaceful and stable life free of worries about war."
He would be willing to meet the North's leadership if the conditions were right, he told his second press conference as head of state.
"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 its banned weapons programmes, which have alarmed the US and the global community, and seen Pyongyang subjected to multiple sets of United Nations sanctions.