The two leaders met again in the Chinese city of Dalian in early May, amid preparations for the historic summit between Kim and US President Donald Trump on June 12 in Singapore.
Trump previously admired North Korea's propaganda channel for lavishing praise on Kim.
"We get along very well, we had good chemistry", Trump said. He has been grumbling that not everyone agrees.
Still, many people on Twitter and beyond found the comment disconcerting, given North Korea's human rights violations and prison camps.
"I have solved that problem.Now we're getting it memorialised and all but that problem is largely solved", Trump said. US officials said it is unclear what types of training involving USA and South Korean troops might constitute "war games" Trump wants halted. "I don't want to see a nuclear weapon destroy you and your family. I want my people to do the same", he added. "And failed they were", Trump said.
Japanese Prime Minister Shinzo Abe on Saturday called on North Korean leader Kim Jong Un to jointly overcome their mutual distrust, as he confirmed ongoing efforts to arrange a Japan-North Korea summit.
And Friday's Fox and Friends interview was not the first time that Trump voiced admiration for Kim.
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"He's his own communications director. When a military official from another government salutes. you return that", Sanders said. Nobody thought we were going to get that. It costs us a lot of money. It was an unprecedented encounter that saw the leader of the world's most powerful democracy shake hands with the third-generation scion of a dynastic dictatorship. "If there's a chance at peace, if there's a chance to end the frightful threat of nuclear conflict, then we must pursue it at all costs", he added.
It was the latest example of a Trump remark about strongmen leaders - delivered in a deadpan style - to fall flat and fuel perceptions among his critics that the president admires autocrats.
An Obama-era agreement with China aimed at curbing economic cyberespionage was reaffirmed by the Trump Administration past year. "I sometimes say the "denuking" of North Korea, and those are attractive words", Trump said in the video.
The challenge of defending the agreement became apparent this past week when Pompeo lashed out at a reporter who asked how the US would verify the North's compliance with the deal.
The two were trying to broker a peace deal that would de-nuclearize the Korean Peninsula, in exchange for economic sanctions lifted on North Korea.
With the broad agreement facing skepticism from allies and the press, Trump is under pressure to sell it.