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Speaking after a meeting of the Inter-Korean Summit Preparatory Committee on Wednesday, Moon said negotiations were continuing ahead of the "historic talks" planned for next month with North Korean dictator Kim Jong Un.
"Through these talks and future talks, we must end the nuclear and peace issue on the Korean Peninsula. It is necessary to make it possible for the two Koreas to live together peacefully without interfering with each other or damaging each other," Moon said Wednesday.
It will be the first time a sitting US President has met with a member of North Korea's ruling Kim family.
No three-way talks have previously been suggested but Moon said if the other summits went well there was a possibility it could lead to high-level meetings. Moon said Wednesday the goals of the upcoming negotiations were denuclearization and "permanent peace" on the Korean Peninsula.
'A sign of change'
Moon's comments came as North Korean state media appeared to make its first positive comments about the United States since the upcoming summit between Trump and Kim was announced.
In an editorial published on North Korea's state broadcaster KCNA, there has been "a sign of change" in relations between the two countries.
In an editorial Wednesday, the broadcaster warned conservatives in the US and South Korea were attempting to derail talks by "peddling groundless stories distorting the truth."
"It is really an expression of small-mindedness for the riff-raffs to spoil the atmosphere, and say this or that, even before the parties concerned are given a chance to study the inner thoughts of the other side and are seated at a negotiating table," the editorial said.
The visit led to speculation a potential meeting between Trump and Kim could take place in Stockholm, a neutral location and an alternative to either Washington or Pyongyang.
CNN's Josh Berlinger contributed to this article.