WASHINGTON—A lawyer for President Donald Trump on Thursday demanded the author and publisher of a new book featuring scathing criticism of the White House halt its publication and apologize, escalating a battle that has consumed the U.S. leader’s return to Washington this week.

In a letter to author Michael Wolff and publisher Henry Holt & Co., Charles Harder said the book contained “numerous false and/or baseless statements,” though it didn’t specify any. He threatened legal action for defamation, invasion of privacy...