Speaking at a news conference Tuesday, Moon said the recent birthday message sent by US President Donald Trump to North Korean leader Kim Jong Un should be considered a good sign.
"Many were worried about a possible military provocation ahead of Chairman Kim Jong Un's birthday, but instead, there was a congratulatory message from President Trump," said Moon, adding that although dialogue between the US and North Korea is not active, relations between the two leaders remain unchanged.
"North Korea has made it clear that the door for dialogue hasn't been shut, even though there was a condition that the dialogue can only resume when North Korea's demands were met," said Moon.
Moon has long positioned himself as something of a mediator between North Korea and the US, a role that has become increasingly difficult as the two sides have failed to make tangible progress in diplomatic talks.
Moon's own attempts to initiate better inter-Korean relations have also suffered, with North Korean officials sidelining those in the South. Moon acknowledged this difficulty, but maintained he was "continuing with optimism."
North Korea has said it will not reopen talks with the US until all its demands are accepted by Washington, and getting Pyongyang back to the negotiating table is likely to a significantly more difficult task than it was after Kim and Trump met for the first time in Singapore in June 2018.
In a statement carried by North Korean state media, Kim Kye Gwan, a veteran diplomat and adviser to the North Korean foreign ministry, said Pyongyang would not consider giving up its nuclear facilities in return for partial sanctions relief.
"There will never be such negotiations as that in Vietnam, in which we proposed exchanging a core nuclear facility of the country for the lift of some UN sanctions in a bid to lessen the sufferings of the peaceable people even a bit," said Kim, referring to the summit between Trump and Kim in Hanoi last year that ended without a deal.
Kim Kye Gwan, who was involved in previous negotiations with the US, said that it would be "absent-minded" to expect a resumption of negotiations.
"Although Chairman Kim Jong Un has good personal feelings about President Trump, they are, in the true sense of the word, 'personal'," he said. "We have been deceived by the US, being caught in the dialogue with it for over one year and a half, and that was the lost time for us."
Trump, Moon and Kim last met in June at the demilitarized zone that divides the two Koreas, but that meeting also failed to yield tangible results.
In the months after, North Korean diplomats repeatedly accused US negotiators of being inflexible, while Washington's envoys have asked Pyongyang to come back to the table.
Working-level talks between the US and North Korea halted last year in Stockholm, Sweden, where US officials said they "had good discussion" while North Korea's top negotiator blamed the ended talks on Washington.