Sen. Chris Coons, Delaware Democrat, said even offering North Korea a summit with the US president is a significant concession, while also saying it's important that North Korea has freed several Americans the country was holding as a confidence-building measure. But Moon said Sunday that he and Kim chose to meet again, rather than have a telephone conversation, as their aides suggested "candid" face-to-face talks between the leaders.
Members of Congress said the devil, as is always the case with North Korea, will be in the details.
Mr Kim has now separately met Mr Moon and Chinese President Xi Jinping twice in the past three months, and both leaders have pledged to strengthen ties with his regime.
The U.S. has frequently called for the "complete, verifiable, and irreversible" dismantlement of North Korea's nuclear weapons program.
Kim Chang Son heads the team from North Korea for the discussion on the summit's security and logistics issues.
Kim Yong Chol, vice chairman of North Korea's ruling Workers' Party Central Committee, watches the closing ceremony. "But Moon interrupted this by reinstating inter-Korean exchanges". Analysts said Mr Moon - who seems to have built trust with Mr Kim through two summits in a month - can help to bridge the gap between the USA and North Korea and mediate if necessary. It is expected that Mr. Kim would make a short stop at Beijing before heading to Korea on Monday, May 28th.
Before canceling the summit last week, Trump said that China had eased up enforcement of sanctions on its border.
Less than a week ago, Trump had announced that he was pulling out of the summit, accusing North Korea of "tremendous anger and open hostility".
In brief remarks to reporters on Saturday night, the president said the lower-level negotiations are "going along very well", though he added his usual caveat: "We'll see what happens".
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He would become the highest-ranking North Korean to visit the United States since General Jo Myong Rok went to the White House to see President Bill Clinton in 2000, part of a denuclearization effort that went nowhere.
The general has always been a right hand man to North Korea's leader, playing a front-seat role during recent rounds of diplomacy aimed at ending the nuclear stalemate on the Korean peninsula. The Washington Post reported that Sung Kim, a former us ambassador to South Korea, is leading the delegation and met Sunday with North Korea's vice foreign minister, Choe Son Hui.
Libyan dictator Moammar Qaddafi agreed in 2003 to give up his weapons of mass destruction, including nuclear arms, in return for sanctions relief. He ended up getting killed at the hands of US-backed rebels less than a decade later.
"I think the two leaders will sit down and they're going to have a great time, because really they have the same personality", said Howard on Sunday.
U.S. and North Korean officials are set to meet in Singapore on Tuesday to discuss security and protocol issues concerning a possible summit between their leaders, a diplomatic source here said.
"Trump's unexpected response totally took Kim by surprise and left the North scrambling to find a way to mend things", Cho Sung-ryul, a senior researcher at the Institute for National Security Strategy, told AFP.
"Kim Jong Un has been anxious for a long time, and his father before him, to meet with the US president and develop the appearance for internal political purposes that he's the peer of the American president.The nuclear weapons give him the feeling that he should be able to do that now", Bennett tells VOA.
Still, there's no sense of a consensus yet on denuclearisation.
Mr Kim and Mr Moon held talks in the demilitarised zone separating their two nations on Saturday in a scramble to salvage the summit.