Moon said: “There’s actually a very tiny window open.”
He said the question “is how to expand this window to lead to actual, meaningful talks”.
Moon added: “I agree that this is the best time for talks with the North.
“Without any talks to follow PyeongChang, the crisis of last year will be repeated. Talks must be started.
“The small window could be wide open depending on how we do.”
North Korea angered the international community with a series of missile launches and threats to destroy the United States and Japan last year.
Its weapons programme is also in defiance of UN Security Council resolutions and has prompted a war of words between Pyongyang and the United States.
However, Kim gave the all clear for talks with his neighbour on the Olympic games and, after a year of mounting tension, diplomacy focused on sport enabled the International Olympic Committee to announce North Korea would send 22 athletes to the February games.
Moon said it was a signal other topics could be discussed between the two nations, and he urged Seoul to open talks on their militaries.
He said: “If it does not take place as agreed, another bout of problems or North Korea’s miscalculation or defiant provocations could follow.”
The former South Korean foreign minister said any talks should include denuclearisation but not a total ban on North Korea’s weapons programs.
But, he also made it clear that there is nothing that will stop Kim if he wants to press ahead with its nuclear ambitions.
He said: “Looking back at the past, the North has frequently gone ahead with provocative remarks or behaviour after major events,”
“You must be well aware that the North has often used peace gestures whenever it was stuck in a difficult situation in the past.
“South Korea needs to be braced for such possibilities and ready to put pressure on North Korea which is made to think that there’s no way out than coming out for negotiations.”
South Korean President Moon Jae-in has also expressed his optimism over a thaw in relations between the two Koreas ahead of the Winter Olympics.
He said it presented a “precious chance” for the United States and North Korea to discuss the North’s weapons programmes.
He said: “No one can be optimistic about how long the current mood for dialogue will last.
“We need wisdom and efforts to sustain the dialogue opportunities… beyond the Olympics so that the inter-Korean talks will lead to talks between the United States and North Korea and other forms of dialogue.”