North Korea's KCNA reported Kim made the remarks and showed his appreciation for South Korean President Moon Jae-in on Wednesday, shortly after meeting with the five-member delegation led by Moon's national security adviser Chung Eui-yong.
"It is our firm stance that a site of peace, free of nuclear threats, will be created," Kim said, according to KCNA.
The state-controlled North Korea news agency said Kim is "committed to denuclearization step by step," or over time, "and to realize the denuclearization of the Korean Peninsula [he proposed] North and South more actively make efforts."
Kim also showed gratitude to Moon, KCNA said.
Kim, "after reading President Moon Jae-in's personally handwritten letter, expressed his gratitude for [Moon's] appraisal of the new progress in North-South relations, and [calls for] prudently overcoming many challenges, while opening a bright future for our people through steadfast will," KCNA stated.
KCNA stated Kim described Moon's letter as "commendable" and that the North Korean leader wanted to relay to Moon Pyongyang's intention to improve the situation "as soon as possible."
News 1 reported Thursday in Pyongyang Chung received approval from the North to open an inter-Korea liaison office in Kaesong, North Korea.
Chung made the remarks at a press conference in Seoul, at the presidential Blue House, according to the report.