Given the stage it had already reached, Pyongyang "may feel like they don't need to test anything for a while", he said.
Journalists from the United States, China, the United Kingdom, Russia and the South would be invited, KCNA added on Saturday.
The test tunnels will be blown up, blocking their entry points, while observation facilities and research institutes will be removed along with guards and researchers, the statement said. It adds that global journalists will be welcomed into the country "to conduct on-the-spot coverage in order to show in a transparent manner the dismantlement of the northern nuclear test ground".
Located in mountainous terrain in the northeast of the country, Punggye-ri is less than 100 miles (160 kilometers) from China.
A ceremony for the dismantling of the facility reportedly has been scheduled between May 23-25.
They will sleep and eat on board the train, but a press centre will be set up so they can "transmit ... about dismantlement of the test ground which they have covered on the spot". Kim was quoted by KCNA as telling the party that its mission has "come to an end".
Punggye-ri hosted all six of North Korea's nuclear tests, the latest of which happened last September and which Pyongyang defined as an H-bomb.
The ICAO said it welcomed North Korea's collaborative approach and would work with adjacent states to facilitate and adopt these proposals.
According to the BBC, the North Koreans have pledged several beginning steps that will be kick started via this ceremony.
South Korea had no immediate response to the statement. The global community has repeatedly condemned North Korea's nuclear and ballistic missile tests and imposed sanctions on Pyongyang to curb its nuclear program. Two of the North Korean missiles passed over the Japanese island of Hokkaido. "We look forward to positive outcomes of the meeting".
"Ahead of the US-North Korea summit, we hope that trust between the leaders of the two countries will be strengthened" by the North's move, the presidential spokesman said.
Secretary of State Mike Pompeo Friday promised the USA would work to rebuild North Korea's sanctions-crippled economy if it agreed to surrender its nuclear arsenal.
The head of the UN's World Food Programme said Saturday it appeared North Korea was "turning a new page in history", following a four-day visit to the country.