Mr. Trump posted throughout the morning about Ms. Manigault Newman, dismissing her as a poor employee but saying that he kept her on despite complaints because she has said nice things about him.

In another post, the president retweeted comments made by Michael D. Cohen, his former personal lawyer, who denied an anecdote in Ms. Manigault Newman’s book, “Unhinged,” claiming that Mr. Trump once chewed up a piece of paper in the presence of both of them to prevent it from being taken by presidential recordkeepers. In the last two weeks, Mr. Trump’s new lawyer, Rudolph W. Giuliani, has painted Mr. Cohen as a serial liar as he has appeared to pose a threat to the president.

Ms. Manigault Newman has also claimed that she was offered a hush-money contract with the Trump re-election campaign for $15,000 a month. A few others who have departed the White House under inauspicious circumstances are receiving that amount.

One White House official insisted that despite the tweets, officials were not bothered by Ms. Manigault Newman’s news media blitz, which included playing for NBC a tape of Mr. Trump calling her. During that call, which she said took place soon after she was fired by John F. Kelly, the White House chief of staff, Mr. Trump claimed not to have known that she was dismissed and that he was dismayed.

Mr. Kelly fired her in December 2017 in a tense meeting in the Situation Room, the most secure conference room in the White House. Ms. Manigault Newman taped that conversation, as well, and released it to NBC, the network on which she appeared during the first season of “The Apprentice” with Mr. Trump.

Officials said they believed that Ms. Manigault Newman might have many dozens of additional audio recordings, and they were preparing for her to release them slowly, to maximize attention on her book. She is not the only West Wing staff member discovered to have been privately taping the president, three current administration officials said; another, now gone, has been caught during Mr. Kelly’s tenure.

Privately and publicly, West Wing aides said they think the tapes revealed more about Ms. Manigault Newman’s disrespect for the institution than it did about her boss.