According to a senior White House official who spoke on the condition of anonymity to describe internal deliberations, this ethos is again behind the White House’s lack of an apology over the remark made by Kelly Sadler, a special assistant to the president, in a meeting last week.

In off-the-cuff comments that were quickly leaked to the news media, Ms. Sadler assessed Mr. McCain’s opposition to Mr. Trump’s nominee for C.I.A. director: “It doesn’t matter,” she said. “He’s dying anyway.”

Two other forces are driving the decision not to apologize, that official said: The first is that White House officials believe that the Obama administration apologized for the United States’ behavior on the world stage too often. And the second is a pervasive feeling of frustration among aides who fear their every word will be leaked to the news media. (An impassioned plea made last week by Sarah Huckabee Sanders, the White House press secretary, to keep internal discussions private was leaked to the website Axios by five aides within hours.)

Anger over leaks starts with the president.

“The so-called leaks coming out of the White House are a massive over exaggeration put out by the Fake News Media in order to make us look as bad as possible,” Mr. Trump said on Twitter on Monday. “With that being said, leakers are traitors and cowards, and we will find out who they are!”

That anger trickles down. When he took to the podium to speak to reporters on Monday, Raj Shah, a deputy White House press secretary, reinforced the idea that the leaks coming from the White House were the main source of frustration internally, not the content of Ms. Sadler’s remarks.

“If you aren’t able, in internal meetings, to speak your mind or convey thoughts or say anything that you feel without feeling like your colleagues will betray you,” Mr. Shah said, “that creates a very difficult work environment. I think anybody who works anywhere can recognize that.”

Mr. Shah added that he understood “the focus on this issue,” but declined to offer specifics that Ms. Sadler’s remarks were being “addressed internally.” Ms. Sadler, who works in the communications office and focuses on immigration, is still at work and is sending emails to the staff as usual, according to a White House official.