North Korea's official KCNA news agency said Kim told the South's envoys that his "fixed stand" was to turn the Korean peninsula into "a cradle of peace without nuclear weapons, free from nuclear threat".
Chung said that Kim's faith in U.S. President Donald Trump is unchanged since their summit in Singapore on June 12.
But the North Korean leader also expressed a "sense of frustration" with the global community for not appreciating what he called Pyongyang's "very significant and meaningful" steps, Chung said. "Chairman Kim especially stressed that he has never talked negatively about President Trump to his staff or anyone else".
Chung also revealed that Kim had expressed exasperation at the global community's doubt over his intentions and its assessment of the steps North Korea had taken.
The next step in nuclear diplomacy is uncertain. The date of the talks, which will come on the eve of a gathering of world leaders at the United Nations at the end of September, was to be released later Thursday.
The phrase "complete denuclearization" - a term long preferred by North Korea - could be read to preclude nuclear-capable USA bombers and submarines from operating near South Korea.
The officials arrived in Pyongyang at 9 a.m. and were driven to the Koryo Hotel, where they were greeted by Kim's right-hand man Kim Yong-chol and Ri Son-gwon, the chairman of the Committee for the Peaceful Reunification of the Fatherland. "He probably saw that there was nothing good in provoking Trump", Lee Byong-chul, of Seoul's Institute for Peace and Cooperation, said. Chung is to meet senior Chinese official Yang Jiechi on Saturday and National Intelligence Service director Suh Hoon, who went to Pyongyang with Chung, is to meet Japanese Prime Minister Shinzo Abe on Monday, according to South Korea's presidential office.
North Korea's Kim Jong-un wants to realize denuclearization during U.S. President Donald Trump's first term - giving a timeline for the first time - and has agreed to a third summit with his South Korean counterpart, Seoul officials said. Kim reportedly complained about the US negotiating in bad faith and regretted the doubts raised about his commitment to peace.
Even in their indirect form, each statement will be parsed for clues about Kim's mindset as North Korea and the U.S. move forward with efforts to resolve a nuclear standoff that just a year ago many feared could lead to war. The display of such sophisticated missiles shows Kim is confident about his military's strength, or he may be trying to use them as leverage in negotiations with the United States, experts say.
Chung, whose official title is presidential national security director, spoke with his USA counterpart, John Bolton, on the phone on Thursday about his trip to North Korea.
And, speaking earlier Thursday in India, Pompeo said an "enormous amount of work" remains.
Though there was no substantive progress in reducing North Korea's nuclear stockpile, North Korea has not appeared to test any missiles or nuclear weapons since the summit.
Under discussion is whether denuclearisation or declaring an end to the 1950-53 Korean War should come first.
South Korea has said American forces should stay even if a peace agreement is signed, while U.S. Defense Secretary Jim Mattis assured Seoul in a June visit of an "ironclad" U.S. commitment to its security, including keeping U.S. troop levels unaltered. The poster at left reads "Let's thoroughly implement the decisions of the April meeting of the Central Committee of the Workers' Party of Korea".