The second trilateral meeting in less than a month followed U.S. Secretary of State Mike Pompeo's visit to Pyongyang on Friday and Saturday where he tried to work out the specifics of denuclearization with senior North Korean officials.
Pompeo said he had won commitments for new discussions on denuclearization and announced a Thursday meeting between US and North Korean military officials on the repatriation of the remains.
State Department Spokesperson Heather Nauert told reporters Saturday that Pompeo and Kim had discussed denuclearization issues along with the repatriation of American remains from the Korean War, adding, "we expect them to live up to their commitments".
Last month, at a historic summit with US President Donald Trump, Kim Jong-un agreed to "work towards complete denuclearization of the Korean Peninsula" in return for security guarantees and an end to a unsafe stand-off with US forces.
The Trump administration has said it would take between 1 and 2 1/2 years to dismantle North Korea's nuclear program. "If I paid attention to the press, I'd go nuts and I refuse to do that". He stressed that "there's still more work to be done" in other areas, much of which would be done by working groups that the two sides have set up to deal with specific issues.
Pompeo said that while he saw progress in Pyongyang, the USA was not relaxing the current sanctions regime or changing its "ironclad" commitment to the defence of allies South Korea and Japan.
Pompeo also said that there would be a meeting next week about the repatriation of remains of American soldiers killed in the Korean War.
Speaking to business executives in the Vietnamese capital Hanoi, Pompeo said he hoped the United States could one day share the same level of partnership with North Korea as it did with Vietnam, a long-time former enemy.
"If those requests were gangster-like, the world is a gangster", Pompeo said, as he noted that the U.N. Security Council has demanded numerous times that the North dispose of its nuclear weapons and end its ballistic missile program.
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North Korea called denuclearization talks with the U.S.
"Give up on disarming North Korea", Lewis said.
But North Korea was careful not to criticize the USA president specifically, emphasizing that "we wholly maintain our trust toward President Trump".
"These are complicated issues but we made progress on nearly all of the central issues", he told reporters, according to Reuters.
"I would like to pay my tribute to the strong leadership you have demonstrated in negotiating with North Korea", Abe said when he met Pompeo at his residence in Tokyo.
"The settlement of the outstanding issues of concern surrounding North Korea, including the nuclear, missile and abduction issues, will be extremely important for Japan and also extremely important for peace and stability in the world", Pompeo told Abe.
It is the first time he has visited North Korea since a summit between Donald Trump and Kim Jong-un in Singapore. Mr Pompeo said he "slept just fine".
"There will be a verification connected to the complete denuclearisation, it's what President Trump and Chairman Kim both agreed to", he added.
Our correspondent at South Korea's foreign ministry, Lee Ji-won, is on the line for us.