For much of this week, President Trump was consumed by a single question. What should he do about his national security adviser, Michael Waltz?

“Should I fire him?” he asked aides and allies as the fallout continued over the stunning leak of a Signal group chat set up by Mr. Waltz, who had inadvertently added a journalist to the thread about an upcoming military strike in Yemen.

In public, Mr. Trump’s default position has been to defend Mr. Waltz and attack the media. On Tuesday, the day after Jeffrey Goldberg of The Atlantic broke the story about being included in the chat, the president said Mr. Waltz was a “good man” who had nothing to apologize for.

But behind the scenes, Mr. Trump has been asking people inside and outside the administration what they thought he should do.

He told allies that he was unhappy with the press coverage but that he did not want to be seen as caving to a media swarm, according to several people briefed on his comments. And he said he was reluctant to fire people in the senior ranks so early in his second term.

But for Mr. Trump, the real problem did not appear to be his national security adviser’s carelessness about discussing military plans on a commercial app, the people said. It was that Mr. Waltz may have had some kind of connection to Mr. Goldberg, a Washington journalist whom Mr. Trump loathes. The president expressed displeasure about how Mr. Waltz had Mr. Goldberg’s number in his phone.

On Wednesday evening, Mr. Trump met with Vice President JD Vance; the White House chief of staff, Susie Wiles; the White House personnel chief, Sergio Gor; his Mideast envoy, Steve Witkoff, and others about whether to stick with Mr. Waltz.

Late Thursday, as the controversy swirled, Mr. Trump summoned Mr. Waltz to the Oval Office. By the next morning, the president signaled to people around him that he was willing to stick with Mr. Waltz, three people with knowledge of the president’s thinking said.

People close to Mr. Trump say Mr. Waltz has been able to hang on in part because some in the administration still support him, and because Mr. Trump has wanted to avoid comparisons to the chaotic staffing of his first term, which had the highest turnover of top aides of any presidential administration in modern history.

And while Mr. Trump can always change his mind, the episode shows Mr. Trump’s willingness to disregard external pressures in his second term, while also grappling with the limits of the loyalty tests he imposed for staff across the administration.

Even before the Signal leak, Mr. Waltz was on shaky footing, viewed as too hawkish by some of the president’s advisers and too eager to advocate for military action against Iran when the president himself has made clear he prefers to make a deal.

An association with Mr. Goldberg, however hazy, gave Mr. Waltz’s opponents more fuel to feed the skepticism.

Some of Mr. Trump closest allies have questioned whether Mr. Waltz, a former George W. Bush administration official, was compatible with the president’s foreign policy. Mr. Waltz had gotten crosswise with Mr. Vance and Ms. Wiles in policy discussions, particularly regarding Iran, according to several people briefed on the matter.

In a statement, the White House press secretary, Karoline Leavitt, said Mr. Trump has a team whose members debate each other but know that he is the “ultimate decision maker.” “When he makes a decision, everyone rows in the same direction to execute,” she added.

Weeks ago, a discussion arose among some aides about whether Mr. Waltz was ideologically aligned with the president. Mr. Trump, who has at times been effusive in private about Mr. Waltz, made clear he did not want to start the cycle of dismissals so early in his second administration, according to two people briefed on the conversation. Mr. Trump, who regretted pushing out his first national security adviser, Michael T. Flynn, after less than a month in 2017, believed it would feed a narrative that he engenders chaos.

After the Signal thread leaked, someone shared on X a snippet of a 2016 video of Mr. Waltz, produced by a group primarily funded by the billionaire Koch brothers. Speaking as a military veteran, Mr. Waltz looked directly into the camera as he condemned Mr. Trump as a draft-dodger and said, “Stop Trump now.” That snippet drew attention from Mr. Waltz’s critics.

By contrast, Defense Secretary Pete Hegseth’s job appears to be safe, even though he shared detailed information about strike times for the attack on Houthi militants in Yemen in the Signal thread. MAGA stalwarts like Charlie Kirk have defended him online.

Mr. Hegseth “had nothing to do with this,” the president said on Wednesday.

Mr. Hegseth survived a bruising confirmation process in the Senate after being pushed through with help from Mr. Vance, and he has a solid relationship with Mr. Trump.

While Mr. Waltz may keep his job, the controversy has reminded Mr. Trump’s aides that the president’s strategy of crisis management — doubling down and denying, no matter how problematic the facts are — does not seem to work as well for them as it has over the years for Mr. Trump.

When the Atlantic story broke, Mr. Waltz denied meeting, knowing or communicating with Mr. Goldberg. But that claim was quickly called into question by photos that surfaced from a 2021 event at the French Embassy in Washington, where Mr. Goldberg and Mr. Waltz were pictured standing next to one another. Mr. Waltz’s allies dismissed the idea that the photo suggested the two men knew each other.

But the reality is that while Mr. Trump has demanded loyalty from his staff, some top officials are longtime Washington hands who have relationships, past experiences and contacts with people whom Mr. Trump despises.

“I would say the principle of getting a bunch of yes men and yes women around him is the guiding principle, a foundation of which is not having, or renouncing, any past that may be proof to the contrary,” said John R. Bolton, who worked as Mr. Trump’s third of four national security advisers and then wrote a revealing book about his time in the White House.

“Anybody who’s been around Washington 10 years, 15 years, has all kinds of backgrounds,” Mr. Bolton said.

In Greenland on Friday, Mr. Vance, who was traveling with Mr. Waltz on a visit to try to apply pressure for the United States to take over the territory, made clear that Mr. Waltz was at fault for adding Mr. Goldberg to the Signal thread.

But Mr. Vance, who was also in the group chat and has defended Mr. Waltz internally in the past, made a point of doing so again. It was a sign that Mr. Trump was ready to move on, for now.

“If you think you’re going to force the president of the United States to fire anybody, you’ve got another think coming,” he said. “President Trump has said it on Monday, on Tuesday, on Wednesday, on Thursday, and I’m the vice president saying it here on Friday, we are standing behind our entire national security team.”