ASPEN, Colo. — The Trump administration said on Friday that it would bar Americans from traveling to North Korea, a month after the death of Otto F. Warmbier, a 22-year-old college student from Ohio who was arrested while trying to leave the country and returned to his parents, more than a year later, in a coma.

The announcement came only hours after Mike Pompeo, the director of the C.I.A., strongly hinted that the United States was considering seeking a regime change in North Korea. Mr. Pompeo told an audience at the Aspen Security Forum on Thursday night that President Trump had ordered him to come up with options that would “separate the capacity” to build and deliver nuclear weapons from “someone who might well have intent,” a clear reference to Kim Jong-un, the country’s leader.

Mr. Pompeo was pressed several times in an interview here on Thursday evening conducted by Bret Stephens, a New York Times columnist, about what he meant by that phrase, and whether it was code for regime change. Mr. Pompeo would not utter that phrase, saying instead, “As for the regime, I am hopeful we will find a way to separate that regime from these” missiles and nuclear weapons.

C.I.A. officials noted that Mr. Pompeo’s language was deliberately ambiguous, and that there were ways to “separate” Mr. Kim from his arsenal without overthrowing the government. Mr. Pompeo, when pressed on the point, noted that there were risks if Mr. Kim left office, because it was unclear who might succeed him.