He has kept a business on the side; attacked the F.B.I., C.I.A. and other institutions he oversees; threatened to use his power against rivals; and waged war against members of his own party and even his own cabinet. He fired the man investigating his campaign and has not ruled out firing the one who took over. He has appealed to base instincts on race, religion and gender as no president has in generations. And he has rattled the nuclear saber more bombastically than it has been since the days of Hiroshima and Nagasaki.

The presidency has served as a vehicle for Mr. Trump to construct and promote his own narrative, one with crackling verve but riddled with inaccuracies, distortions and outright lies, according to fact checkers. Rather than a force for unity or a calming voice in turbulent times, the presidency now is another weapon in a permanent campaign of divisiveness. Democrats and many establishment Republicans worry that Mr. Trump has squandered the moral authority of the office.

“We’re seeing the presidency completely and utterly transformed in a way I don’t think we’ve seen since before the Civil War,” said Jeffrey A. Engel, the director of the Center for Presidential History at Southern Methodist University and the author of “When the World Seemed New” about President George Bush. “Trump is arguing that we need to take care of my enemies. I really can’t think of any precedent.”