Pompeo was briefing North Asian leaders on Trump's first-of-its-kind summit with Kim, meeting with South Korean President Moon Jae-in before heading to Beijing later to talk with China's Xi Jinping.
In an interview recorded in Singapore but broadcast on the US television channel, Fox News, late on Wednesday in the US, Trump said that a withdrawal of US troops from South Korea had not been discussed at the summit.
Lasting peace has obvious benefits for China, especially in bolstering the development of its rust-belt and landlocked northeast which borders North Korea and would suffer in the even of conflict. "I would anticipate it will be fairly quickly after we return to our home countries".
Trump has been criticized for already announcing the halting of "war games", or military exercises, with South Korea, a move long sought by Pyongyang.
"A year ago the pundits & talking heads, people that couldn't do the job before, were begging for conciliation and peace - 'please meet, don't go to war.' Now that we meet and have a great relationship with Kim Jong Un, the same haters shout out, 'you shouldn't meet, do not meet!'" Baier noted that Trump had praised Kim as "a very talented person" and had said they have good chemistry.
He added that it would be impossible to verify completely whether North Korea completely denuclearized. "North Korea has great potential for the future!", he wrote.
Japan is expected to contribute towards the costs of North Korea's denuclearisation but only after the International Atomic Energy Agency restarts inspections, a spokesman said on Wednesday.
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North Korean viewers had to wait nearly 20 minutes into the program for Trump's first appearance.
In his post-summit press conference, Trump made the surprise announcement that the United States would halt joint military exercises with its security ally Seoul - a concession Pyongyang has sought for decades.
The secretary of state dismissed a report by North Korean state media that Mr Trump and Mr Kim had agreed to a "step-by-step" process of nuclear dismantling.
But there was some skepticism about the summit's outcome "I'm afraid that many Japanese people are not so satisfied with the agreement".
Speaking in a wood-paneled office aboard Air Force One, Baier put it to the U.S. president that Kim was "a killer".
News that Kim did not utter North Korea's usual claim has started raising hopes among Japanese government officials that there may be room to resume bilateral negotiations with Pyongyang.
He said Kim affirmed an "unwavering commitment to complete denuclearization of the Korean Peninsula" in a signed document.
"We got a lot more done [Tuesday] than I ever thought possible", he said of the meeting with Kim.
The Rodong Sinmun, the ruling Workers' Party newspaper, focused on photographs of Kim and Mr Trump shaking hands.