When asked if the U.S. president had made a "chess playing move" and if Kim's statement had changed Trump's view on the talks, Town said that the entire situation, including the Trump letter itself, cancelling the historic summit, came as a surprise, even though he had hinted that "it was possible to pull out of the meeting".
The two leaders reiterated hopes for a successful North Korea-US summit after Trump abruptly canceled a meeting between the two countries planned for June 12 in Singapore.
A statement from North Korea's state news agency KCNA said Mr. Kim expressed "his fixed will" on the possibility of meeting Mr. Trump as previously planned.
"It's moving along very nicely". He wrote: "We are having very productive talks with North Korea about reinstating the summit which, if it does happen, will likely remain in Singapore on the same date, June 12th, and, if necessary, will be extended beyond that date".
"I am urging (North Korea and the US) to exchange such intentions, and to confirm the counterpart's will through direct communications". "I'd like to say that the fact that North Korea and the USA agreed to have a summit and working-level talks indicates that the US has already confirmed the North's intentions".
The South Korean president called on both sides to hold working-level talks that may help resolve these differences.
A White House team will leave as scheduled for Singapore this weekend to prepare for the possible summit, a White House spokeswoman said on Saturday.
She also said it was up to the Americans whether they would "meet us at a meeting room or encounter us at nuclear-to-nuclear showdown". "Kim and Choe know each other well - both were part of their respective delegations that negotiated the 2005 denuclearization agreement through the six-party framework".
The spontaneous offer by Kim to meet, and Moon's quick acceptance, shows how close the two leaders have become in a short period of time.
A denuclearized North Korea is the ultimate goal, but we can't expect to get there by insisting on it as a precondition.
The US-South Korea alliance could take a hit if Moon intentionally exaggerated Kim's commitment to denuclearisation, according to Namkoong, who also teaches inter-Korean politics at Hankuk University of Foreign Studies.
At their first meeting on April 27, Kim and Moon first announced "complete denuclearisation of the Korean Peninsula" and permanent peace, which Seoul has tried to sell as a meaningful breakthrough to set up the summit with Trump. -North Korea summit in Singapore are still on track and the details are being worked out.
Sung Kim, who was born in South Korea, was a key diplomat in the 2005 six-party talks. Earlier this week, in Washington, President Moon said he anticipates the resumption of inter-Korean talks after the Max Thunder air exercises end Friday.
The meetings are expected to continue on Monday and Tuesday and are focused on the issue of North Korea's nuclear weapons program, it said.
The talks "are going very, very well", Trump said.
Sung, a South Korean born diplomat, is a former nuclear negotiator with North Korea and current US ambassador to the Philippines.
Saturday's summit marked the fourth meeting between the leaders of the two Koreas since they were divided at the end of the World War II in 1945.