On Monday, Ms. Clifford’s lawyer added new charges to the suit she filed: that the president’s lawyer defamed Ms. Clifford in denying her claims; that he and Mr. Trump pursued the deal to specifically help Mr. Trump’s election prospects; and that he then structured the agreement to shield from public view what was, effectively, an illegal $130,000 campaign gift.
In discussions with allies and some aides, Mr. Trump has privately railed against Ms. Clifford, and insisted that she is not telling the truth. He has reminded advisers that he joined an effort to enforce financial penalties against Ms. Clifford, whose TV interview on Sunday night was hyped throughout the weekend on the cable news channels that Mr. Trump watches obsessively.
But there has been no debate among Mr. Trump’s advisers about the best course for him: just keep quiet about a story that would only be fueled by a presidential tweet or a comment about the women shouted above the roar of Marine One.
Keeping a lid on Mr. Trump is never easy, especially when he is eager to hit back at his adversaries.
In the days after an “Access Hollywood” video exposed his own lewd comments about women during the final month of the campaign, Mr. Trump responded by showing up at his debate with Hillary Clinton with three women who had accused Bill Clinton of sexual improprieties.
As a candidate, and as president, Mr. Trump has eagerly attacked just about all of his enemies and accusers, often with colorful nicknames like “Little Rocket Man” for the North Korean leader, “Crazy Joe Biden” or “Sloppy Steve” Bannon.
But for now, it appears that the president is listening to — and accepting — his advisers’ warnings on the dangers of speaking out about the women, much the way he followed the advice of his lawyers for a year not to attack Robert S. Mueller III, the special counsel in the Russia inquiry.
Recently, he has ditched that advice, attacking Mr. Mueller and his team directly on Twitter. That leaves only his alleged mistresses and President Vladimir V. Putin of Russia as people who are immune to Mr. Trump’s Twitter trash-talk.
Raj Shah, a deputy White House press secretary, declined to say “what the president may or may not have seen” on television Sunday night, though he said that Mr. Trump denies the allegations that Ms. Clifford made in the CBS interview.
“I’ll just say that he’s consistently denied these allegations,” Mr. Shah said. “The president doesn’t believe that any of the claims that Ms. Daniels made last night in the interview are accurate.”
Mr. Trump dined at his Mar-a-Lago estate in Florida on Saturday evening with Michael D. Cohen, his lawyer and longtime aide who is at the center of the Clifford scandal, according to three people familiar with the get-together. The president scheduled the meeting himself, surprising his aides with it a short time before Mr. Cohen arrived, people familiar with the meeting said.
Melania Trump, too, has been silent about the allegations. Asked to react to the interviews, Stephanie Grisham, Mrs. Trump’s spokeswoman, said: “She’s focusing on being a mother, she’s quite enjoying her spring break and she’s focused on future projects.”
It is not clear whether Mr. Trump watched a similar tell-all interview on CNN on Thursday evening, when Karen McDougal, a former Playboy model, alleged a 10-month romantic affair with Mr. Trump in which they repeatedly had sex.
Sunday’s interview with Ms. Clifford contained few surprises but some humiliating details, such as Ms. Clifford saying she was not attracted to Mr. Trump, and her recollection of spanking him. Virility and strength are key traits that the president likes to project, and he once gloated about a New York Post headline quoting a friend of his second wife, Marla Maples, who recalled Ms. Maples saying that Mr. Trump was the “Best Sex I’ve Ever Had.”
In the interview, Ms. Clifford said that she had flirted with Mr. Trump in 2006 at a celebrity golf tournament in Lake Tahoe. She said Mr. Trump had compared her favorably to his daughter during the flirtation, and that she had intercourse with Mr. Trump.
She also alleged that an unknown person whom she believed to be connected to Mr. Trump and Mr. Cohen threatened her in a parking lot in 2011, telling her, “leave Trump alone. Forget the story.” Then looking at her infant daughter, he added, “That’s a beautiful little girl. It would be a shame if something happened to her mom.”
Asked by Anderson Cooper whether she had anything to say to Mr. Trump, if he was watching Sunday night, Ms. Clifford said, “He knows I’m telling the truth.”
Even that has not prompted Mr. Trump to directly address the central allegations from Ms. Clifford and Ms. McDougal — that the president cheated on his wife shortly after Mrs. Trump gave birth to their son.
Mr. Trump did type out a vague “Fake News” tweet on Monday morning, although it is unclear to what he was referring.
Beyond the details of the alleged encounters, Mr. Trump’s advisers have been urging the president to keep quiet about the legal wrangling concerning Ms. Clifford and Ms. McDougal.
Ms. McDougal, who accepted $150,000 from the parent company of the National Enquirer to keep quiet about her alleged affair with Mr. Trump, is suing the company to be released from the contract. Mr. Cohen has acknowledged paying Ms. Clifford $130,000 in the days before the 2016 election to keep quiet about her allegations.
Mr. Shah said at the White House on Monday that “I can say categorically that, obviously, the White House didn’t engage in any wrongdoing.”
Asked about why Mr. Trump’s lawyer would pay Ms. Clifford $130,000 if her allegations were false, Mr. Shah said that “false charges are settled out of court all the time.” He referred further questions about the case to Mr. Cohen.
The lawyer for Ms. Clifford has aggressively argued that his client is not bound by the nondisclosure agreement that she signed, in part because Mr. Trump himself never signed the document. Michael Avenatti, the lawyer, has repeatedly used Trumplike insinuations to suggest that Ms. Clifford has digital evidence of the intercourse.
“We have a litany of more evidence in this case, and it’s going to be disclosed, and it’s going to be laid bare for the American public,” Mr. Avenatti said in an interview Monday morning on ABC’s “Good Morning America.”
Last week, Mr. Avenatti tweeted a picture of a CD or DVD with the suggestive caption: “If a picture is worth a thousand words, how many words is this worth???? #60minutes #pleasedenyit #basta.”
Even that has not prompted a presidential retort — yet.
An earlier version of this article misstated the title of Raj Shah. He is a deputy White House press secretary, not the White House press secretary.