When host Chris Wallace pressed him about how close North Korea is to being able to hit the US mainland, Pompeo said that it was alarming but hard to define.
Sen. Lindsey Graham, R-S.C., welcomed Trump's pugnacious approach, arguing that numerous president's critics failed to stop North Korea from developing a nuclear weapon that could hit the United States.
But Mr Pompeo denied that a threat of a nuclear conflict was imminent, saying: "I've heard folks talking about being on the cusp of a nuclear war".
The call came after Trump made fresh threats against North Korea on Friday, declaring the USA military "locked and loaded" and warning Kim that he "will regret it fast" if he takes any action against US territories or allies.
White House officials have insisted the investigation is not created to apply additional pressure on China as it relates to North Korea despite the president's previous remarks that he would be more amenable on trade if China stopped Pyongyang's nuclear program.
But Trump on Friday appeared to set another red line - the mere utterance of threats - that would trigger a USA attack against North Korea and "big, big trouble" for Kim.
But he rejected talk of the USA being on the "cusp of nuclear war".
The CIA chief described Mr Kim as "rational" and responsive to "adverse circumstances". "This is something that has a risk of getting to a very, very bad place, so America needs to take this very seriously".
"I think we're not closer to war than a week ago, but we are closer to war than we were a decade ago", National Security Adviser H.R. McMaster told ABC News' "This Week".
Mr Trump said the United States military was "locked and loaded", while Pyongyang has accused him of "driving" the Korean peninsula to the "brink of a nuclear war".
"Let's see what he does with Guam", Trump told reporters, referring to North Korean dictator Kim Jong-un. Trump has said he would not allow Pyongyang to develop a nuclear weapon capable of hitting the United States.
President Trump wrote on Twitter on Friday that U.S.
The war of words comes as North Korea continues its missile and nuclear programs..
He conducted two in July, so it wouldn't surprise me if there was another missile test, ' Pompeo said on Fox News Sunday.
A Chinese state-run newspaper said on Friday that China should remain neutral if North Korea launches an attack that threatens the United States, sounding a warning for Pyongyang over its plans to fire missiles near Guam.