Mr Kim also asked the envoy to relay a message to the US, while voicing hopes to end their hostile ties before US President Donald Trump's term ends in January 2021.
South Korea's National Security Adviser Chung Eui-yong said North Korean leader Kim Jong-un "reconfirmed his determination to completely denuclearise" the peninsula, and expressed his willingness for close cooperation with Pyongyang and the United States in that regard.
Chung's top agenda item was arranging another summit meeting between Kim and South Korean President Moon Jae-in.
Now, the South Korean envoy has a message for Trump from Kim, who apparently described the steps his country has made toward denuclearization as "very significant and meaningful", Yonhap reported.
Chung said Kim showed "frustration over the doubt raised by some parts of the worldwide community about his willingness to denuclearize, and asked us to convey his message to the United States".
Stephen Biegun, newly-appointed USA envoy for the North, said last month Kim had promised "final, fully verified denuclearisation" at the Singapore summit.
The summit being planned will be the first time in more than a decade that a South Korean leader has visited the North Korean capital.
Google Assistant Can Now Speak Multiple Languages Interchangeably
Google can handle you asking a question in one language and then following up with another question in a different language. In addition to supporting multiple languages, the assistant will use machine learning to enhance user experience.
The State Department also announced Thursday that its new special envoy for North Korea policy, Stephen Biegun, would be travelling to South Korea, China and Japan next week, his first assignment since his appointment last week as point-man for diplomatic efforts with Pyongyang.
"The North's official media said today that Kim Jong Un has reaffirmed his commitment to a nuclear-free Korean Peninsula and the suspension of all future long-range missile tests", NPR's Rob Schmitz reported.
Chung and Suh Hoon, the director of South Korea's National Intelligence Service, traveled last week to Pyongyang to lay groundwork for the third meeting between Kim and South's President Moon Jae-in. "There have been no nuclear tests or missile tests... but work on making the strategic shift continues", Pompeo said on a visit to New Delhi.
South Korea's Yonhap News on Thursday quoted analysts who took Kim's remarks as a positive sign. Kim said he'd take "more active" measures toward denuclearization if his moves are met with corresponding goodwill measures, Chung said. The article said the North has shown "goodwill and generosity" through actions such as returning US war remains and dismantling a nuclear testing ground, but that the USA has failed to respond similarly.
"The countries agreed to review the implementation of the Panmunjom Declaration and discuss the future direction of its implementation, and to discuss practical ways to establish lasting peace and ensure joint prosperity on the Korean Peninsula, especially denuclearize the Korean Peninsula", he told a nationally televised press conference.
North and South Korea remain technically at war as the 1950-53 Korean War ended in a ceasefire.
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 said such a declaration would not imply a withdrawal of American forces or a weakening of the US-South Korean military alliance, Chung said.