South Korean officials told reporters earlier today that Kim wants to continue the negotiations he and the US have engaged in since the summit in Singapore.
'Chairman Kim said that although the dialogue between the us and North Korea is experiencing some difficulties, his trust in President Trump continues, especially at times like this, ' according to Chung Eui-yong, South Korea's director of national security and the leader of the envoys.
The trove of comments from Kim, including his commitment to a nuclear-free Korean Peninsula and to the suspension of all future long-range missile tests, were relayed by top South Korean security officials returning from meeting him in Pyongyang as well as the North's propaganda specialists.
Chung - Moon's national security advisor - flew to Pyongyang on Wednesday to meet with Kim and deliver Moon's letter to the North's leader.
"Chairman Kim. expressed frustration over the doubt shown by some parts of the worldwide society about his will", Chung said.
Trump responded Thursday by tweeting, "Kim Jong Un of North Korea proclaims 'unwavering faith in President Trump.' Thank you to Chairman Kim".
"Kim also made it clear that he needs some kind of proof Trump has abandoned the U.S.'s hostile policy before moving toward denuclearization".
But Mr Kim apparently disagreed, insisting to Mr Chung that the steps taken by his country so far, including the dismantlement of a nuclear test site, are significant and meaningful.More news: Donald Trump attacks union leader on Labor Day
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Yonhap's analysts saluted the South Korean government's role as a mediator in denuclearization talks and suggested North Korea might have pumped the breaks on Pompeo's trips to Pyongyang to give South Korean officials an opportunity to remain involved in negotiations.
"(Chairman Kim) said his faith in President Trump remains unchanged.
The vague Singapore agreement said the two sides would work towards denuclearisation but did not include any timeline, details or mechanisms to verify the process.
Kim "reaffirmed his determination to completely denuclearise" the peninsula, and expressed his willingness for close cooperation with South Korea and the United States in that regard, Chung said.
The North Korean leader also pledged to "achieve the denuclearisation of the Korean peninsula in the first official term of President Trump", Mr Chung said. "He said he's pre-emptively taken steps necessary for denuclearisation and wants to see these goodwill measures being met with goodwill measures".
The U.S. Embassy in Seoul on Thursday said it had no information to share on the matter. They also worry that an end-of-war declaration could weaken North Korea's incentive for denuclearisation, while raising questions about some 18,500 US troops stationed in South Korea, a legacy of the Korean War.
At a press conference, the envoys said Mr Kim told them it was his firm will to work with South Korea to achieve a lasting peace settlement.
Kim brushed off such worries on Wednesday, and said declaring an end of the Korean War has nothing to do with the U.S.
Not only that they manged to hear directly from the regime's leader, where Pyongyang stands on denuclearization and peace efforts. Post-summit nuclear negotiations between Washington and Pyongyang were rocky and quickly settled into a stalemate.