North Korea still has nuclear weapons.
After his meetings in Seoul, Pompeo left for Beijing, where he was expected to meet Chinese President Xi Jinping and Foreign Minister Wang Yi.
He said Kim affirmed an "unwavering commitment to complete denuclearization of the Korean Peninsula" in a signed document.
Washington remained committed to the "complete, verifiable and irreversible" denuclearisation of North Korea, Pompeo added, after the historic US-North Korea summit in Singapore drew criticism for its vague wording on plans for Pyongyang to give up its nuclear weapons.
Trump also declared on social media on Wednesday that "there is no longer a nuclear threat from North Korea", after his meeting with Kim.
"I will face (North Korea) directly and work toward resolving the abduction issue", he told the families.
The 42-minute-long program, narrated by North Korea's most famous newscaster, Ri Chun-hee, was broadcast on state-run television Thursday, two days after the historic summit in Singapore and a full day after Kim returned home to his country's capital, Pyongyang.
Moon later said South Korea would be flexible when it came to military pressure on North Korea if it was honest about denuclearisation. He says Trump and Kim Jong Un had a "blunt conversation" about changes needed for North Korea to rejoin the world community.
Tokyo has reacted with concern at Trump's surprise announcement that military exercises with South Korea are to be halted, saying that such drills are "vital" for East Asian security.
Late past year, for example, she announced North Korea's test of what it said was a hydrogen bomb, telling viewers it was a "perfect success".
"If (Abe's) visit to Pyongyang in August proves hard", he could hold talks with Kim on the sidelines of the Eastern Economic Forum in Russia's Vladivostok in September, the Yomiuri said.
Many lawmakers from both parties, while unready to declare the summit a diplomatic victory or defeat, remained skeptical the US could successfully negotiate a deal toward peace with Kim - but are letting the process play out. "However, the president has not ignored the bad things that have been done by the North Korean regime".
Kang said South Korea and the United States shared the same goals and approach to achieving denuclearization.
Gen. Kim Do-gyun, center, speaks to the media before leaving for the border village of Panmunjom to attend South and North Korea meeting, at the Office of the South Korea-North Korea Dialogue in Seoul, South Korea, today.
-South Korea joint military exercises if talks between the Democratic People's Republic of Korea (DPRK) and the United States continue.
Sakie Yokota, whose daughter Megumi was kidnapped at age 13, told reporters she was encouraged by Trump's talks with Kim and said she had urged Abe to resolve the issue quickly.
The joint annual U.S. -South Korean air combat exercises.
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