Pompeo also said that the problem has been ongoing through previous USA administrations, but he argued President Donald Trump was making strides to effect change.
"Nothing is imminent. But be careful, the increased likelihood of a nuclear missile strikes the United States is a very unsafe threat", added the director of the u.s. central intelligence agency.
North Korea warned foreign diplomats to leave Pyongyang in 2013 when it suspended work at a joint inter-Korean industrial park and threatened missile strikes on U.S. Pacific bases, notably in Guam and Hawaii.
"He conducted two in July so it wouldn't surprise me if there's another missile test", Pompeo said.
"Every time they test a missile, or if they are a test nuclear missile, they are gaining in expertise, and we can say that they progress at an alarming rate", said Mr. Pompeo on Fox News, when asked about the possibility of a missile north Korean nuclear strike on american soil.
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".
In a separate interview on ABC News, Trump's national security adviser, H.R. McMaster, struck a similar tone. The CIA chief described Kim as "rational" and responsive to "adverse circumstances".
"We're all looking to get out of this situation without a war", he added.
China's president, Xi Jinping, made a plea for cool-headedness in a phone conversation with Trump on Saturday, urging both sides to avoid words or actions that could worsen the situation.
In response, Mr Trump said North Korea should expect "big, big trouble" if anything happened to Guam.
Tuesday: "North Korea, best not make any more threats to the United States", Mr Trump tells reporters. China is the North's biggest economic partner and source of aid, but says it alone can't compel its wayward ally to end its nuclear and missile programs.
The tough talk capped a week in which long-standing tensions between the countries risked abruptly boiling over.
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.
The North then came out with a threat to lob four intermediate-range "Hwasong-12" missiles near Guam, a tiny USA territory some 2,000 miles (3,200 kilometers) from the North's capital, Pyongyang.