Mr Chung also cited Mr Kim as saying that North Korea is unable to conduct any more nuclear tests, despite several reports that the regime is secretly continuing its nuclear programme.
Pompeo visited Pyongyang in July, after which North Korea accused him of making "unilateral and gangster-like demands for denuclearisation" while showing little interest in ending the war.
"It is the case that there is still an enormous amount of work to do", Pompeo told a news conference in New Delhi.
Seoul's chief envoy to the North also said Kim had referred to the dismantling of the Dongchang-ri missile site as signifying his intentions to permanently stop long-range ballistic missile development.
Any progress could depend on whether Moon's envoys were able to coax a stronger verbal commitment from North Korea on denuclearization to help put the nuclear talks between the United States and Pyongyang back on track.
Chung Eui-yong, head of the presidential National Security Office, walks to board an aircraft as he and others in a delegation leave for Pyongyang, North Korea, at a military airport in Seongnam, south of Seoul, South Korea, Wednesday, Sept. 5, 2018.
"Chairman Kim. expressed frustration over the doubt shown by some parts of the worldwide society about his will", Chung said.
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He even expressed regret that the global community does not appreciate such meaningful steps taken by his country, the South Korean envoy said.
"He said he's pre-emptively taken steps necessary for denuclearisation and wants to see these goodwill measures being met with goodwill measures", Chung said.
Pyongyang has said the United States needs to reciprocate North Korea's goodwill gestures, which also include the return of USA war remains, by stating an official end to the 1950-53 Korean War.
Mr Kim was also pleased to receive a personal letter from Mr Moon, delivered by Mr Chung, KCNA added. Negotiations since then have been rocky and settled into a stalemate.
While Trump and Kim Jong Un pledged during their historic summit in June to "work toward complete denuclearization of the Korean Peninsula", they didn't define what that meant or offer a timetable for carrying it out.
Seoul and Pyongyang both want a declaration to formally end the 1950-53 Korean War. Signing a peace treaty without a disarmament deal also carries risks for the USA, because it could legitimize Kim's control over half of the peninsula and undermine the rationale for stationing 28,000 or so American troops on the peninsula.
"The United States shouldn't delay any further an end-of-war declaration, which the USA president promised at the Singapore summit", the North's official Rodong Sinmun newspaper said in an editorial.
They also discussed the complex process of dialogue between Pyongyang and Washington, Efe news reported. Dongguk University professor Koh Yu-hwan said it was significant that Kim has finally committed to a timetable for denuclearization, even though he was vague on exactly what he planned to do by the end of President Trump's first term.