John F. Kelly, his longest-serving White House chief of staff in his first term, has said that Mr. Trump would tell his press aides to publicly repeat something that he had just made up. When Mr. Kelly would object, saying, “but that’s not true,” Mr. Trump would say, “but it sounds good.”

Stephanie Grisham, who served as a White House press secretary in the first term, once recalled that Mr. Trump would tell aides that “as long as you keep repeating something, it doesn’t matter what you say.” And that trickled down to the staff. “Casual dishonesty filtered through the White House as though it were in the air-conditioning system,” she wrote in her memoir.

Anthony Scaramucci, a former Trump ally who served briefly as his White House communications director, said on Friday that Mr. Trump believes dishonesty works. Mr. Trump, he said, is at “50 years of distorting things and telling lies and he is at 50 years of getting away with it, so why wouldn’t he make the lies bigger and more impactful in this last stretch?”

Mr. Trump, who repeatedly disparaged media fact-checking during last year’s campaign, does not back off after misleading statements and lies are exposed. Instead, he tends to double down, repeating them even after it’s been reported that they are not true.

After reporters determined that the $50 million for condoms story was untrue, Mr. Trump not only repeated it, he increased the supposed total to $100 million. Nor did he back down after falsely claiming that U.S.A.I.D. had provided grants to media organizations as “a ‘payoff’ for creating good stories about the Democrats,” even after learning the money was simply for subscriptions.