The agreement was announced in Pyongyang by North Korean leader Kim Jong Un and South Korean President Moon Jae-in at the close of the second of their three-day summit.
"Kim Jong-un has agreed to allow nuclear inspections, subject to final negotiations, and to permanently dismantle a test site and launch pad in the presence of worldwide experts", Trump claimed hyperbolically.
While Kim didn't commit Wednesday to giving up his arsenal of nuclear weapons and ballistic missiles that pose a threat to the USA mainland, he did promise to dismantle North Korea's main rocket launch site in the presence of worldwide experts, and offered to shutter its Nyongbyon nuclear site.
Pompeo's statement came after the North and South Korean leaders met for a third summit and declared that progress had been made in efforts to normalize relations.
His meetings with North Korean leader Kim Jong Un appear to have put wobbly U.S.
Moon said Kim had also told him the closure of a nuclear weapons test site at Punggye-ri could be subject to worldwide verification. Speaking of the need for North Korea to take denuclearization measures, Moon said "the US should accordingly take corresponding measures to guarantee the security of North Korea step by step".
Kim reported from Seoul. "We're not out of the woods yet when it comes to North Korea", he said, but "we have some time".
Kim reportedly told South Korean diplomats at a meeting in early September that his aim is to denuclearize by the end of Trump's first term in 2021.
"It was inevitable we were going to war in North Korea, and now, . the relationships, I have to tell you, at least on a personal basis, they're very good".
The leaders of the two Koreas agreed on steps aimed at advancing North Korea's denuclearization.
Kim also wants a second summit with U.S. President Donald Trump as soon as possible.
Washington has demanded concrete action, such as a full disclosure of North Korea's nuclear and missile facilities, before agreeing to Pyongyang's key goals, including an easing of global sanctions and an official end to the Korean War. Their trip to the mountain on the North Korean-Chinese border, and the striking photo-op that will resonate in both Koreas, followed the announcement of wide-ranging agreements on Wednesday that they trumpeted as a major step toward peace. He didn't indicate in his brief remarks whether the United States would be willing to take further steps to encourage North Korean action on denuclearisation.
What else did Moon's visit achieve?
Trump also tweeted that North Korea has agreed to conduct searches for the remains of soldiers who went missing during the Korean War. The war still technically continues because it ended in 1953 with a cease-fire, not a peace treaty.
President Moon of South Korea has urged the United States to end the impasse in denuclearisation talks with North Korea by formally declaring an end to hostilities in the Korean War (Daniel Hurst writes).
South Korea's national anthem opens with a reference to the volcano while for the North it is the alleged birthplace of Mr Kim's father and grandfather. There will also be resistance to rolling back sanctions adopted by the USA unilaterally and through the United Nations without significant progress toward denuclearization and a clearer idea of exactly what North Korea has in its nuclear arsenal and where all its facilities are located.
"The need for USA forces in Korea is not affected at all".