The adviser, Lt. Gen. H. R. McMaster, told the staff of the National Security Council on Thursday, in his first “all hands” staff meeting, that the label “radical Islamic terrorism” was not helpful because terrorists are “un-Islamic,” according to people who were in the meeting.

That is a repudiation of the language regularly used by both the president and General McMaster’s predecessor, Michael T. Flynn, who resigned last week after admitting that he had misled Vice President Mike Pence and other officials about a phone call with a Russian diplomat…

“This is very much a repudiation of his new boss’s lexicon and worldview,” said William McCants, a senior fellow at the Brookings Institution and the author of “The ISIS Apocalypse.”

“McMaster, like Obama, is someone who was in positions of leadership and thought the United States should not play into the jihadist propaganda that this is a religious war,” Mr. McCants said.