The militaries of South Korea and the US have also carried out their annual joint exercises more discreetly ahead of the upcoming historic meeting between Kim and US President Donald Trump in Singapore on June 12.
Pompeo said he had a "good" conversation with North Koreans and did his best to convey the U.S. message to them.
The test ground will be completely closed after the process, KCNA said. For its part, North Korea wants the lifting of sanctions and for the U.S.to withdraw the 28,500 troops it has stationed in South Korea.
Leader Kim Jong-un recently pledged to suspend the country's nuclear program, but little is known about its existing arsenal.
The United Nations human rights investigator on North Korea called on Thursday for six South Korean nationals in custody there to be freed, voicing concern over conditions of their detention.
Following the Moon-Kim summit, Moon's office said Kim was willing to disclose the process to worldwide experts, but the North's statement Saturday didn't include any mention about allowing experts on the site.
North Korea would have to provide details about its nuclear facilities before the global community could even develop a plan to dismantle the country's program.
The summit will be the first meeting ever between a sitting USA president and the leader of North Korea.
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During his summit with South Korea's President Moon Jae-in last month, The North Korean leader Kim Jong-un said he would invite experts and journalists from South Korea and the USA to watch the dismantling of the Punggye-ri facility in North Hamgyong Province.
Kim had revealed plans to shut down the nuclear test site during his summit with South Korean President Moon Jae-in last month.
Much of this range would be far higher than officials from the United States and South Korea estimate.
In North Korea's bombastic rhetoric, "denuclearization" has, for years, been a byword for USA troop withdrawals from South Korea.
Kim declared his nuclear force as complete in December, following North Korea's most powerful nuclear test to date in September and three flight tests of ICBMs created to reach the USA mainland.
Both Kang and Pompeo stressed that their goal is to achieve a "complete" and "verifiable" denuclearization of the Korean peninsula. Estimates suggest the value of North Korea's basic minerals - coal, copper, etc. - ranges from $6 to $10 trillion total, not counting the rare earth metals. With U.S. help, those countries recovered from the devastation of conflict.
An underground test of what was claimed by North Korea to be a hydrogen bomb shook the surrounding landscape so violently, it changed the shape of an entire mountain. "North Korea's nuclear test center will be discarded in order to ensure the transparency of the suspension of the nuclear test".