Donald Trump in particular has promised "fire and anger" at North Korea.
But the intelligence chief also said he saw no imminent threat of North Korea attacking the USA with such a nuclear weapon, although he expected the rogue nation's missile program would continue despite global sanctions.
North Korea, for its part, threatened to shoot four missiles towards the island of Guam, a strategic outpost of the u.s. forces in the Pacific, where are stationed about 6,000 american soldiers.
In a separate interview on "Fox News Sunday", Pompeo was asked about the nature and degree of threat to the US mainland in light of Kim's continuing drive to develop North Korea's missile and nuclear capacities.
"I am quite confident that (North Korean leader Kim Jong Un) will continue to try to develop his missile program, so it wouldn't surprise me if there was another missile test".
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.
National security adviser H.R. McMaster said Trump has asked for a report on what could happen next in the country. The CIA chief described Kim as "rational" and responsive to "adverse circumstances". He also will discuss military options in the event the "diplomatic and economic pressurization campaign" fails.More news: Macquarie Boosts Prudential plc (LON:PRU) Price Target to GBX 1977
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"We're all looking to get out of this situation without a war", he added.
Referring to Kim, President Trump added: "If he utters one threat ... or if he does anything with respect to Guam or any place else that's an American territory or an American ally, he will truly regret it, and he will regret it fast".
Tuesday: "North Korea, best not make any more threats to the United States", Mr Trump tells reporters.
Trump warned last week that North Korea would be met with "fire and fury" if it continued to threaten his country.
State-run China Central Television quoted Xi as telling Trump the "relevant parties must maintain restraint and avoid words and deeds that would exacerbate the tension on the Korean Peninsula".
CIA Director Mike Pompeo said Pyongyang was moving at an "ever-alarming rate" with its weapons programme and another missile test would not be surprising.
But Trump on Friday appeared to set another red line - the mere utterance of threats - that would trigger a US attack against North Korea and "big, big trouble" for Kim.