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 and other claims, which legal experts said would face steep hurdles in court.

Rather than halting the book’s scheduled Jan. 9 publication, Henry Holt said it would advance it to Friday “due to unprecedented demand.” In a tweet, Mr. Wolff said, “Thank you, Mr. President.”

Mr. Wolff’s book, “Fire and Fury: Inside the Trump White House”—excerpts of which were published in New York Magazine on Wednesday—features criticism of the president and some of his top advisers, including several family members. It extensively quotes former White House chief strategist Steve Bannon, who called a June 2016 meeting between top Trump campaign aides and a Russian lawyer “treasonous” and aired concerns that missteps by aides could lead to legal jeopardy for the president.

“Mr. Trump hereby demands that you immediately cease and desist from any further publication, release or dissemination of the book, the article, or any excerpts or summaries of either of them,“ Mr. Harder wrote. He requested “a full and complete retraction and apology.”