And the United States introduced a fresh round of sanctions on the North for violating global law by using a banned chemical weapon to assassinate Kim Jong-nam, the eldest son of former North Korean leader Kim Jong-il and brother of Kim Jong-un.
Moon expressed hope for resumption of dialogue between the USA and the North, which he earlier called a prerequisite to resuming multilateral negotiations aimed at ridding the North of nuclear weapons. Trump wrote in a Twitter post on Tuesday.
North Korean state media pictures of the delegation's extended meeting with Kim in Pyongyang showed the North's leader in a jovial mood, smiling and shaking hands enthusiastically.
An increase in diplomatic efforts with North Korea has seen a delegation attend the Winter Olympics in Pyeongchang in February, and on Tuesday Mr Kim met an envoy from Seoul.
Tensions rose to the highest level in years over North Korea's nuclear and missile programmes, which it pursues in defiance of UN Security Council resolutions, with shrill, bellicose rhetoric coming from both Kim Jong Un and Trump.
"I think they're honest also because of the sanctions and what we're doing with respect to North Korea", he told reporters on March 6.
South Korea's goal was the denuclearisation of North Korea, nothing less, said Moon in comments distributed by the Blue House. North Korea is already under severe USA and United Nations sanctions and so yesterday's decision will have little impact on the country.
But South Korean President Moon Jae-in sounded a note of caution Wednesday over the North's offer of denuclearization talks, saying it was "too early to be optimistic".
Kim Jong Un is willing to give up nuclear weapons if the security of his regime is guaranteed, according to South Korea, after he reportedly said it was the last wish of his father.
Malaysia has never accused the North Korean regime of conspiring to kill Kim and has worked to avoid larger political implications during the trial which is ongoing.
But he warned complete denuclearisation was "a heavy lift" involving intensive weapons inspections inside North Korea and he was sceptical of this outcome.
"In terms of the meeting with South Korea and also with the DPRK (North Korea), we don't have a play-by-play of that just yet". In the same statement from President Moon Jae-in's office, it revealed that it will be graced by the two states' leaders. I think we're having very good dialogue, and we're going to certainly find out pretty soon what's happening, but we have made progress, there's no question about it.