During a Thursday meeting with Trump, they delivered an invitation from Kim for an unprecedented summit between the USA and the North - plus a separate, special message to the American leader.
"This meeting won't take place without concrete actions that match the promises that have been made by North Korea".
As a matter of fact, Chung Eui-yong and Suh Hoon, the special envoys to the USA, were not initially scheduled to meet with President Trump on Thursday.
Dutch Ambassador Karel van Oosterom, who chairs the council's North Korea sanctions committee, told reporters "we have to continue implementing the sanctions as they stand".
A Realmeter poll showed Monday that 73 percent of 500 South Koreans surveyed said they welcomed North Korea's change of attitude.
Moon and Kim are expected to talk about a proposal for restarting communications between the North and South Korean militaries. "I may leave fast or we may sit down and make the greatest deal for the world".
Trump administration officials have said there will be no more conditions imposed on North Korea before a meeting of the two nations' leaders.
"However, I would strongly urge the Administration to remember that Kim Jong Un, like his father and grandfather before him, have long sought a visit from the president of the United States to enhance their own prestige and justify their risky pursuit of nuclear weapons".
Davis, a Republican, noted previous administrations tried to entice North Korea's government with financial incentives, and yet North Korea had no intention of doing away with its nuclear program.
"We look forward to the smooth [talks between the two Koreas] and dialogue between North Korea and the U.S.", Xi was quoted as saying.
He stressed that North Korea must stick to the commitments that were relayed by South Korean officials who met with Kim last week and then came to Washington and briefed Trump.
"If they do decide to denuclearize, it will be a temporary denuclearization that they will agree to", said Carranza.
Cheong Seong-chang is an expert on North Korea at the Sejong Institute in South Korea.
Trump said he believes North Korea will abide by its pledge to suspend missile tests while he prepares for the summit. Pyongyang declared past year that it had pulled off the remarkable feat of becoming a nuclear power - a move thought to be aimed at gaining leverage in talks with the U.S.
In Geneva, the United Nations investigator on North Korea told the world body's Human Rights Council that any progress in the nuclear and security dialogue must be accompanied by talks on human rights violations, including political prison camps.
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