The White House’s demand that Macmillan cease publication of a controversial new book about President Donald Trump and his administration is “flagrantly unconstitutional” and runs afoul of the First Amendment, said John Sargent, chief executive of the publisher.

Mr. Sargent made the comments in an internal letter to staffers that was first reported by an industry newsletter, Publishers Lunch. The book, “Fire and Fury: Inside the Trump White House,” was written by Michael Wolff and published by Henry Holt & Co., a Macmillan-owned...