U.S. secretary of state Mike Pompeo arrived at Osan Air Base south of Seoul from Singapore early on Wednesday evening.
The KCNA report - which was also carried by the Rodong Sinmun, official newspaper of the ruling Workers' Party - also claimed that the president pledged to suspend military drills with South Korea, and lift sanctions on the North.
"You know, we're spending a fortune, every couple of months we're doing war games with South Korea, and I said, 'What's this costing?' We're flying planes in from Guam, we're bombing empty mountains for practice", Trump said.
"Not all of that work appeared in the final document", Pompeo said.
Experts believe the North is close to being able to target the entire US mainland with its nuclear-armed missiles, and while there's deep skepticism that Kim will quickly give up those hard-won nukes, there's also some hope that diplomacy can replace the animosity between the USA and the North.
"We are working with the regional countries on getting this (deal) going. It's because North Korea has been belligerent", said Kim Taewoo, former president of the Korea Institute for National Unification in Seoul.
There were worries, especially in Tokyo and Seoul, which have huge U.S. military presences, about Trump agreeing to halt United States military exercises with South Korea, which the North has long claimed were invasion preparations.
The leaders spoke briefly to the press - all smiles from Kim Jong-un - and then went into their private conversations.
Some credit Trump's tough line on North Korea, amounting to nuclear brinkmanship, for bringing Kim to the negotiating table and potentially solving the problem of a nuclear-armed Pyongyang. Bob Corker, R-Tenn., the chairman of the Senate Foreign Relations Committee.
"That's a great example of hyperbole", he added. So we look nice and handsome and thin?
He told ABC in an interview, "I would love to have him at the White House, whatever it takes". It's hard to discern yet if anything concrete occurred. "I think there's some validity to that school of thought with the exception (of) once those dictators have nuclear weapons". After a day filled with smiles and handshakes watched around the world, the United States "committed to provide security guarantees" to North Korea. "The real negotiations have yet to unfold", Republican Senator John Cornyn told VOA.
The lack of a definitive timeframe or verification mechanism for North Korea's nuclear disarmament prompted some former USA diplomats to question the utility of the summit and suggested Trump's tactics could undermine Washington's alliances with Seoul and Japan.
Critics, however, saw the handshake and Kim's earlier moonlight stroll as evidence Trump was helping to legitimize Kim as his equal on the world stage even though the North Korean regime has been accused of horrific rights abuses.
The document promised "complete denuclearization of the Korean Peninsula" without detailing exactly what that would entail.
Just after its start, both men walked toward each other from opposite ends of a colonnade, pausing before a row of alternating USA and North Korean flags for a lengthy handshake as cameras flashed and video and photos were beamed around the world.
"On the other hand, Kim wants a peace treaty to replace the armistice he wants a guarantee from the United States that they won't bring about regime change and he wants a lifting of sanctions so North Korea can join the worldwide economic community and get on with it".
One of the four key points agreed to by President Trump and North Korean leader Kim Jong Un is to help repatriate the remains of Americans killed in action during the Korean War.
Steve Herman and Bill Gallo contributed.
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