“Nobody’s going to fight the United States militarily over the future of Greenland,” Mr. Miller told Jake Tapper, the CNN host, after being asked repeatedly whether he would rule out using military force.

The remarks were part of a vocal push by Mr. Miller, long a powerful behind-the-scenes player in Trump administration policy, to justify American imperialism and a vision for a new world order in which the United States could freely overthrow national governments and take foreign territory and resources so long as it was in the national interest.