"Nothing is imminent. But be careful, the increased likelihood of a nuclear missile strikes the United States is a very risky threat", added the director of the u.s. central intelligence agency.
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. No intelligence that would indicate we are in that place today".
This AP file photo shows CIA Director Mike Pompeo.
"We've seen the Chinese now say for among the first times that they believe the correct answer has to be a denuclearized peninsula", Pompeo said on "Fox News Sunday". "They expand the envelope", he said.
The former top intelligence official in the Obama administration said denuclearization was a "nonstarter" for the North Korean government, which he said viewed its nuclear weapons program as its "ticket to survival".
Pompeo said he could not get into specifics but said that North Korea's progress has gone on for decades. "But make no mistake about it ... the increased chance that there will be a nuclear missile in Denver is a very serious threat".
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.
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Pompeo said the rhetoric from Trump was geared at sending a message to North Korea and letting the isolated nation know that the United States policy of "strategic patience" had come to an end.
Mr Pompeo said he was "quite confident" that North Korean leader Kim Jong-un would "continue to try to develop" the country's weapons programme.
"He responds to adverse circumstances", he said.
National security adviser H.R. McMaster said Trump has asked for a report on what could happen next in the country.
He said he doesn't think the U.S.is closer to war than a week ago, but closer to war than a decade ago. "We're taking all possible actions short of military action, to resolve this very grave threat to the united states and the world".
"The United States military is always locked and loaded", he said.
Some former security and defense officials have said that Trump's rhetoric - including a threat of "fire and fury" and an assertion days later that the US military was "locked and loaded" in the face of North Korea's provocations - have made a volatile situation worse. "The most effective way of preserving peace is to be prepared for war".