So with the summit in Singapore possibly back on, President Moon pledged to call or meet with his North Korean counterpart whenever necessary.
On Thursday, Trump abruptly cancelled the proposed summit meeting with the North Korean leader on June 12 in Singapore and blamed Pyongyang's "tremendous anger" and "open hostility" for his dramatic decision. Trump told reporters that they are still considering Singapore as the venue for their talks. He said there is a "lot of good will" and denuclearization of the Korean Peninsula would be "a great thing".
Pictures from the summit show Mr Moon and Mr Kim shaking hands as well as embracing, and reveal Mr Kim brought along his sister, Kim Yo Jung. It allowed Moon to push for a US-North Korean summit that he sees as the best way to ease animosity that had some fearing a war previous year.
Moon huddled with North Korean leader Kim Jong Un on Saturday and he said the despot agreed that the historic summit should go off as planned.
"He. expressed his intention to put an end to the history of war and confrontation through the success of the North-US summit and to cooperate for peace and prosperity", Moon told reporters in Seoul on Sunday.
Mr. Moon said while Mr. Kim is committed to denuclearisation, North Korea is not convinced it can trust security guarantees from the United States.
"Even though they share the same resolve, there need to be discussions regarding the roadmap for how to make it happen, and that process could be tough", he said, declining to define "complete denuclearization". The first summit was held at the Peace House, a South Korean building opposite Panmungak.
"It's really gotten to the point where if you walk away from your computer or your Twitter feed for more than 10 minutes you find yourself hopelessly out of date", says the Heritage Foundation's Bruce Klingner, who's a former Central Intelligence Agency analyst on the Koreas.
Moon said he held Saturday's impromptu summit - the second between the two sides in a month - after Kim asked for a meeting "without any formality".
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 North hasn't openly repeated those same demands after Kim's sudden outreach to Seoul and Washington.
"Chairman Kim agreed on that", he added. "They simply stood us up". Moon's journey to Washington was largely to prepare Trump for the summit just weeks before it was set to take place. DPRK is the acronym for the North's official name, the Democratic People's Republic of Korea.
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Following an unusually provocative 2017 in which his engineers tested a purported thermonuclear warhead and three long-range missiles theoretically capable of striking mainland United States cities, Kim has engaged in a flurry of diplomatic activity in recent months. A top North Korean official later blasted the comments as "unlawful and outrageous".
The prime minister said he plans to hold talks with Trump over the telephone soon after returning to Japan.
The talks between North and South Korea was initially supposed to occur earlier this month until it was called off by the North, citing military exercises conducted by the South and the U.S.
Howard X, who is a musician by training and said he still produces Brazilian music sung in Chinese, said his partner known as Dennis Alan impersonates Trump.