Mike Pompeo said Pyongyang was moving at an "ever-alarming rate" with its weapons programme and another missile test would not be surprising.
But he warned that Washington's "strategic patience" was over.
Both sides have used hostile rhetoric, with President Donald Trump threatening "fire and fury" on the North.
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.
When asked about how close the North was to being able to deploy a nuclear weapon that could hit the US, he said: "They're closer".
In an interview with Fox News Sunday he added: "They're moving towards that [goal] at an ever-alarming rate."
Long-standing tensions over North Korea's nuclear programme worsened when it tested two intercontinental ballistic missiles in July. That prompted a new round of UN economic sanctions, which angered Mr Kim's regime.
Mr Trump said the US military was "locked and loaded", while Pyongyang has accused him of "driving" the Korean peninsula to the "brink of a nuclear war".
Tuesday: "North Korea, best not make any more threats to the United States," Mr Trump tells reporters. "They will be met with fire and fury like the world has never seen"
Wednesday: Mr Trump boasts that the US nuclear arsenal is "more powerful than ever"
Thursday: He says that his "fire and fury" warning maybe "wasn't tough enough". Asked what would be tougher than fire and fury, he replies, "you'll see"
Friday: The US president warns that military solutions are "locked and loaded" should North Korea "act unwisely".
Trump administration's mixed messages
Who said it: Trump or Kim?
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. I've seen no intelligence that would indicate that we're in that place today."
Several countries have expressed concern with the escalation of the crisis. China, North Korea's only major ally, has urged restraint.
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.
In response, Mr Trump said North Korea should expect "big, big trouble" if anything happened to Guam.
There is no imminent threat of a nuclear war with North Korea, the director of the US Central Intelligence Agency said, despite rising tensions.