Trump, who said this week that North Korea's nuclear program is "very substantial, " has also softened his rhetoric - suspending military exercises and scaling back his demands for what North Korea must do to receive relief from sanctions. He said negotiations would recommence "in the next week or so".
He also said that the North Korean leader agreed to destroy a "major" missile testing site. "He was not leaving the summit without claiming he made a deal", Kimmel said.
On Thursday, the rival Koreas held rare high-level military talks to discuss reducing tensions across their heavily fortified border.
Secretary of State Mike Pompeo walks with Gen. Vincent K. Brooks, commander of U.S. Forces Korea, as he arrives at Osan Air Base in Pyeongtaek, South Korea, on Wednesday.
USA officials said it was unclear what types of training involving US and South Korean troops might cross into Trump's now forbidden zone of "war games".
North Korea will of course be demanding that the sanctions be lifted.
Pompeo was scheduled to travel next to Beijing before returning to Washington. Chris Murphy, D-Conn., and Tammy Duckworth, D-Ill., would prevent Trump from withdrawing troops from South Korea unless the secretary of defense says it's in the interest of national security and that it would not undermine the security of allies in the region.
Last month, Trump ordered the Pentagon to issue options for reducing the American presence in South Korea, despite his administration's assurances that they were not a bargaining chip in the Kim talks. But big, joint U.S.More news: Watch Painfully Shy 13-Year-Old Singer Slay On ‘America’s Got Talent’
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There has been deep scepticism about the agreement, with observers saying it lacked detail on how North Korea would give up its nuclear weapons and how that process would be verified.
In the joint statement, North Korea only agreed to "work toward" denuclearization.
North Korea is believed to possess more than 50 nuclear warheads, with its atomic program spread across more than 100 sites constructed over decades to evade worldwide inspections.
But he said that was no longer the case, and everyone can "sleep well tonight".
Sceptics of how much the meeting achieved pointed to the North Korean leadership's long-held view that nuclear weapons are a bulwark against what it fears are USA plans to overthrow it and unite the Korean peninsula. "North Korea is no longer a nuclear threat, the president says, Kim Jong-Un is trustworthy, & "our country's biggest enemy" is journalists".
"Let me assure you that "complete" encompasses verifiable in the minds of everyone concerned".
For South Korea particularly, the suspension of the annual military exercises came as a surprise. -South Korean drills was met with concern. "So he's a very smart guy, he's a great negotiator, but I think we understand each other". He told reporters that if the USA concludes they no longer are, the freeze "will no longer be in effect".
Earlier today, North Korean state media reported that Trump made concessions to Kim that were not in the statement signed by the leaders - including Trump agreeing to "the principle of step-by-step and simultaneous action" rather than the USA administration's prior demands for rapid denuclearization.
In Japan, the prospect of canceled U.S. He said he planned to continue sharing the view with Washington and Seoul. It's unclear whether the president informed USA allies in the region of his plan to end the "war games", as he called them, prior to his declaration.