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. "President Trump has made it clear that it is his intention to protect the American people".
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.
President Trump issued yet another provocative warning of military action against North Korea on Friday, the third time in a week that he has suggested he was ready to strike the small, isolated Asian country that has been developing nuclear weapons capable of reaching the United States.
North Korea's military has reacted angrily by stating its preparedness to "contain" the U.S. bases on the Pacific island of Guam with missile strikes.
Both sides have used hostile rhetoric, with President Donald Trump threatening "fire and fury" on the North.
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.
North Korea announced on Thursday plans to fire missiles near the US Pacific territory of Guam, even though there was no indication an attack is imminent.
At the end of July, North Korea test-fired an improved intercontinental ballistic missile (ICBM), a Hwasong-14, that could strike the U.S. mainland, purportedly, as far east as Chicago.
Tuesday: "North Korea, best not make any more threats to the United States", Mr Trump tells reporters.
Chinese Foreign Ministry spokesperson Geng Shuang made the remarks in a press statement in response to the recent spat between the United States and North Korea over the situation on the peninsula.
Meanwhile, North Korea said on Saturday that almost 3.5 million workers, party members and soldiers volunteered to join or rejoin its army to resist new U.N. sanctions and to fight against the United States in the current geopolitical tension between Pyongyang and Washington.
North Korea is expected to lose up to $1.7 billion a year under the latest sanctions adopted by the U.N. Security Council on August 5, according to Ri, who now lives in the United States and responded via phone and email.
National security adviser H.R. McMaster said Trump has asked for a report on what could happen next in the country. He defected to South Korea in October 2014 and has lived in the United States since March 2016.