Baier pressed Mr. Trump on his praise for Kim, pointing to the North Korean leader's murderous regime record.
Secretary of State Mike Pompeo said he expects North Korea to take the major steps toward nuclear disarmament during Donald Trump's first term, as the US president tweeted that there's "no longer a Nuclear Threat from North Korea".
"Hey, when you take over a country, tough country, with tough people, and you take it over from your father, I don't care who you are, what you are, how much of an advantage you have", the president continued.
But was it a language Kim Jong-un understands?
I could see that the excitement of the day and the punishing travel schedule had begun to wear on President Donald Trump by the time he came to the back of Air Force One to greet the travelling press before departing Singapore.
North Korea, Trump said Tuesday, has agreed to destroy a major missile engine testing site. "I could go through a lot of nations where a lot of bad things were done".
When South Korea's president shuttled between North Korea and the United States to broker their first-ever summit, he faced both praise and criticism over whether he was a peace-making mediator or was helping North Korea find ways to weaken US -led economic sanctions. But if Trump seeks re-election in 2020, his government is likely to apply more pressure on North Korea to make substantial progress in denuclearization, which could bring the nuclear issue to another critical point, said Shin Beomchul of Seoul's Asan Institute for Policy Studies.
On the way forward, Pompeo said, "I don't know exactly what the timing will be for our next conversation with the North Koreans".
"The way I interpret this first [Trump-Kim] meeting, which was surprising to everybody, is that it's like two boxers touching gloves". He's a very smart guy, a great negotiator.
He said it's meaningful in itself that the leaders of the United States and North Korea met, talked and signed an agreement that will carry more weight and significance than any pact previously made between the wartime foes.
"I have a very strong relationship with President Xi of China".
Bong Youngshik, a professor at Seoul's Yonsei University, said it's too early to predict how Trump's cancellation of the military drills will play out in future nuclear negotiations. And they probably believe, correctly, that this was a good thing.
Rounding out Trump's positive appraisal of leaders with a tight grip on power, the president was asked about his relationship with Vladimir Putin and his call to reinstate Russian Federation into the G-7 alliance. Would you get out of the Ukraine, get out of Ukraine, you shouldn't be there?
"I will tell you, as an example, if he were at that meeting I could ask him to do things that are good for the world, that are good for the country, that are good for him", Trump said. If I'm sitting like I was with the others, for instance the new prime minister of Italy.
With the headline: "Meeting of the century opens new history in DPRK-US relations", the North's ruling Workers Party official daily Rodong Sinmun splashed no fewer than 33 pictures across four of its usual six pages. "He agrees with me on Putin by the way".