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 top US intelligence official said on Sunday he would not be surprised if North Korea tested another missile, given that it had two tests in July, amid rising tensions between the two nations.
USA intelligence does not indicate an imminent nuclear war with North Korea, the chief of the Central Intelligence Agency said Sunday, after a week of bellicose rhetoric between the two sides.
Trump warned last week that North Korea would be met with "fire and fury" if it continued to threaten his country.
Asked how anxious people should be, Pompeo told Fox News Sunday: "Nothing imminent".
He added that he was confident North Korea would continue to develop its missile capabilities under its leader Kim Jong-Un, "so it wouldn't surprise me if there was another test".
Long-standing tensions over North Korea's nuclear programme worsened when it tested two intercontinental ballistic missiles in July.
Later, Trump stressed that the USA military is "locked and loaded" for a potential conflict.
Tuesday: "North Korea, best not make any more threats to the United States", Mr Trump tells reporters.
"I don't think military action is imminent, but we're on a collision course with North Korea", Graham said on "Fox News Sunday".
"It's that straightforward", he added, "What we need from an intelligence perspective, what is most important is that our communications are clear that the fella who intends to inflict pain on the United States of America understands the USA position in an unambiguous way".
Pompeo also said that the problem has been ongoing through previous US administrations, but he argued President Donald Trump was making strides to effect change.
Several countries have expressed concern with the escalation of the crisis. In response, North Korea announced a detailed plan to fire ballistic missiles towards Guam, a USA territory in the Pacific.
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 an interview with German newspaper group RND, Gabriel said the maneuvers "could lead to North Korea using the opportunity for renewed provocation, for example, by firing an intermediate-range missile at Guam".