US President Donald Trump cancelled the summit, scheduled to be held in Singapore on 12 June, but later suggested it might still go ahead.
In his address, Moon said Sunday that Kim had "once again made clear his will for the complete denuclearization of the Korean Peninsula", he said, "and expressed his willingness to end the history of war and confrontation and cooperate for peace and prosperity through a successful summit with the United States".
Trump added: "We'll see what happens".
Asked about the abrupt cancellation of the North-U.S. summit, Cho did not elaborate, saying he will look into what Trump said in the letter and figure out the overall situation. -North Korea summit on track, said he delivered a message of Trump's "firm will" to end the hostile relationship with North Korea and pursue bilateral economic cooperation.
That revelation signals that Kim keenly wants the U.S. summit, and that Moon is happy to play the role of an intermediary between Pyongyang and Washington. So we're looking at June 12th in Singapore.
Moon, who returned to Seoul on Thursday morning after meeting Trump in Washington in a bid to keep the high-stakes U.S. "They very much want to do it".
"We have inwardly highly appreciated President Trump for having made the bold decision, which any other USA presidents dared not, and made efforts for such a crucial event as the summit", Kim Kye Gwan's statement said.
(LEAD) South Korea vows to faithfully implement summit agreement with NK
An official at South Korea's presidential office says it was North Korea who reached out first.
USA officials had said, after Trump's announcement that the summit was off, that North Korean officials had not been responding to their communications.
It remains unclear whether Kim will ever agree to fully abandon his nuclear arsenal in return, despite Moon's insistence that Kim can be persuaded to abandon his nuclear facilities, materials and bombs in a verifiable and irreversible way in exchange for credible security and economic guarantees.
President Moon maintained that Kim is committed to "complete" denuclearization, but acknowledged that Pyongyang and Washington may have differing expectations of what denuclearization means.
"A meeting was held because officials of both countries thought that meeting face-to-face would be better than a phone call", Mr. Moon said.
He praised Kim for announcing a moratorium on nuclear and missile tests, as well as the closing of the country's nuclear test site this week.
The Saturday summit between Moon and Kim became the second time the two leaders met in less than two months, and it followed a groundbreaking meeting in April. At that meeting, they declared they would work toward a nuclear-free Korean peninsula and a formal end to the 1950-53 Korean War.