Kim's message was conveyed to USA national security adviser John Bolton over the phone at 8 p.m. on Thursday, Korean time, according to Cheong Wa Dae spokesman Kim Eui-kyeom.
North Korea, on the other hand, insists that Japan must "settle the past", or compensate for the suffering of the Korean people under Japan's 1910-1945 colonial rule of the Korean Peninsula, before the two countries settle the abduction issue. "Chairman Kim especially stressed that he has never talked negatively about President Trump to his staff or anyone else".
At the upcoming summit, the leaders of the two Koreas will also discuss ways to further reduce military tension between their countries.
South Korean national security advisor Chung Eui-yong, who met with Kim, said the North Korean leader also emphasized that his "trust in Trump remains unchanged", the comment which led to the USA president's tweet.
Chung went on to relay Kim's statement that he has never negatively assessed the United States president at any time.
It was recently reported that Shigeru Kitamura, head of the Cabinet Intelligence and Research Office, visited Vietnam in July in an attempt to make contact with Kim Song Hye, head of the united front tactical office of the North Korean ruling party's United Front Department.
North Korea's official KCNA news agency said Kim told Chung and other envoys that it was his "fixed stand" to turn the Korean peninsula into "the cradle of peace without nuclear weapons and free from nuclear threat". "I say it a hundred times, no missiles, no rockets, no nuclear testing".
Pompeo, visiting New Delhi, said there was a long road ahead and "an enormous amount of work to do" on the denuclearisation process.
Kim, however, expressed to Chung that he was frustrated by skepticism in the worldwide community over his commitment to denuclearisation.
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Trump's campaign rallies are often characterised by raucous interactions among supporters, Trump, and, sometimes, protesters. Trump said similar things when he tweeted about the op-ed on Wednesday - though he suggested the Times made up the report.
Kim also reaffirmed his nation's commitment to "actively engage in denuclearization if the countermeasures are taken simultaneously" and "expressed frustration that his goodwill is not being properly delivered to the worldwide community".
"It would not be very appropriate for Chairman Xi to appear on the podium standing next to Kim Jong Un under those circumstances", said Zhao Tong, a fellow at the Carnegie-Tsinghua Center for Global Policy.
And it's a case of "you've got mail" for U.S. President Donald Trump.
That summit will be a crucial indicator of whether larger nuclear negotiations with the United States will proceed.
Moon's liberal government, which is eager to continue engagement with North Korea, also wants the declaration.
Thursday, Chung told reporters about his talks with Kim. Seoul has indicated an interest in Kim and Trump meeting in NY, and Trump, who is facing growing domestic turmoil, has hinted that another summit could happen. South Korean officials say the summit will focus on how to achieve the denuclearization of the Korean Peninsula.
This is the first time the North Korean leader laid out a potential deadline for dismantling nuclear weapons, the development of which pushed the region to the brink of military confrontation a year ago.
During the 70 years that the Kim family has ruled, North Korea's 30-plus massive military parades have been used as much for propaganda, intimidation and internal unity as for commemorating important anniversaries.
North Korea's message has been delivered to White House National Security Adviser John Bolton, Seoul said. He said not enough progress had been made toward denuclearization.
Those officials said earlier Thursday that Kim still has faith in Trump's commitment to ending their nations' hostile relations, but is frustrated by questions about his willingness to denuclearize and wants his "goodwill measures" to be met in kind.