Even before he disclosed secret battle plans for Yemen in a group chat, information that could have endangered American fighter pilots, it had been a rocky two months for Defense Secretary Pete Hegseth.

Mr. Hegseth, a former National Guard infantryman and Fox News weekend host, started his job at the Pentagon determined to out-Trump President Trump, Defense Department officials and aides said.

The president is skeptical about the value of NATO and European alliances, so the Pentagon under Mr. Hegseth considered plans in which the United States would give up its command role overseeing NATO troops. After Mr. Trump issued executive orders targeting transgender people, Mr. Hegseth ordered a ban on transgender troops.

Mr. Trump has embraced Elon Musk, the billionaire chief executive of SpaceX and Tesla. The Pentagon planned a sensitive briefing to give Mr. Musk a firsthand look at how the military would fight a war with China, a potentially valuable step for any businessman with interests there.

In all of those endeavors, Mr. Hegseth was pulled back, by congressional Republicans, the courts or even Mr. Trump.

The president made clear last Friday that he had been caught by surprise by a report in The New York Times on the Pentagon’s briefing for Mr. Musk, who oversees an effort to shrink the government, but also denied that the meeting had been planned.

“I don’t want to show that to anybody, but certainly you wouldn’t show it to a businessman who is helping us so much,” Mr. Trump said.

But Mr. Hegseth’s latest mistake could have led to catastrophic consequences.

On Monday, the editor in chief of The Atlantic magazine, Jeffrey Goldberg, wrote that he had been inadvertently included in an encrypted group chat in which Mr. Hegseth discussed plans for targeting the Houthi militia in Yemen two hours before U.S. troops launched attacks against the group.

The White House confirmed Mr. Goldberg’s account. But Mr. Hegseth later denied that he put war plans in the group chat, which apparently included other senior members of Mr. Trump’s national security team.

In disclosing the aircraft, targets and timing for hitting Houthi militia sites in Yemen on the commercial messaging app Signal, Mr. Hegseth risked the lives of American war fighters.

Across the military on Monday and Tuesday, current and retired troops and officers expressed dismay and anger in social media posts, secret chat groups and the hallways of the Pentagon.

“My father was killed in action flying night-trail interdiction over the Ho Chi Minh Trail” after a North Vietnamese strike, said the retired Maj. Gen. Paul D. Eaton, who served in the Iraq war. “And now, you have Hegseth. He has released information that could have directly led to the death of an American fighter pilot.”

It was unclear on Tuesday whether anyone involved in the Signal group chat would lose their jobs. Republicans in Congress have been wary of running afoul of Mr. Trump. But Senator Roger Wicker, Republican of Mississippi and the chairman of the Armed Services Committee, indicated on Monday that there would be some kind of investigation.

John R. Bolton, a national security adviser in the first Trump administration, said on social media that he doubted that “anyone will be held to account for events described by The Atlantic unless Donald Trump himself feels the heat.”

In his article, Mr. Goldberg said he was added to the chat by Michael Waltz, Mr. Trump’s current national security adviser.

On Tuesday, Mr. Trump defended Mr. Waltz. “Michael Waltz has learned a lesson, and he’s a good man,” Mr. Trump said in an interview on NBC.

The president added that Mr. Goldberg’s presence in the group chat had “no impact at all” and that the Houthi attacks were “perfectly successful.”

To be sure, some of Mr. Hegseth’s stumbles have been part of the learning process of a high-profile job leading a department with an $850-billion-a-year budget.

“Secretary Hegseth is trying to figure out where the president’s headed, and to run there ahead of him,” said Kori Schake, a national security expert at the American Enterprise Institute. But, she added, “he’s doing performative activities. He’s not yet demonstrated that he’s running the department.”

Peter Feaver, a political science professor at Duke University who has studied the military for decades, said the Signal chat disclosure “raises serious questions about how a new accountability standard might apply: How would he handle a situation like this if it involved one of his subordinates?”

On Monday, Mr. Hegseth left for Asia, his first trip abroad since a foray to Europe last month in which he was roundly criticized for going further on Ukraine than his boss had at the time. He posted a video on social media of himself guarded by two female airmen in full combat gear as he boarded the plane at Joint Base Andrews. The show of security was remarkable. Not even the president is guarded that way as he boards Air Force One.

When he landed in Hawaii several hours later, Mr. Hegseth criticized Mr. Goldberg as a “so-called journalist” and asserted that “nobody was texting war plans, and that’s all I have to say about that.”

Mr. Hegseth’s stumbles started soon after he was sworn in to lead the Pentagon on Jan. 25.

In his debut on the world stage in mid-February, he told NATO and Ukrainian ministers that a return to Ukraine’s pre-2014 borders, before Russia’s first invasion, was “an unrealistic objective” and ruled out NATO membership for Ukraine. A few hours later, Mr. Trump backed him up while announcing a phone call with President Vladimir V. Putin of Russia to begin peace negotiations.

Facing blowback the next day from European allies and President Volodymyr Zelensky of Ukraine, Mr. Hegseth denied that either he or Mr. Trump had sold out Ukraine. “There is no betrayal there,” Mr. Hegseth said.

That was not how even Republican supporters of Mr. Hegseth saw it. “He made a rookie mistake in Brussels,” Mr. Wicker said about the secretary’s comment on Ukraine’s borders.

“I don’t know who wrote the speech — it is the kind of thing Tucker Carlson could have written, and Carlson is a fool,” Mr. Wicker said, referring to the conservative media personality and former Fox News host.

Mr. Hegseth sought to recover later in the week, saying he had simply been trying to “introduce realism into the expectations of our NATO allies.” How much territory Ukraine may cede to Russia would be decided in talks between Mr. Trump and the presidents of the warring countries, he said.

Last week, Mr. Hegseth again got crosswise with Mr. Wicker over reports that the Trump administration was planning to withdraw from NATO’s military command and reduce the number of troops deployed overseas in addition to other changes to the military’s combatant commands.

Mr. Wicker and Representative Mike Rogers, Republican of Alabama and the chairman of the House Armed Services Committee, said in a statement that they were concerned about reports that the Defense Department might be planning changes “absent coordination with the White House and Congress.”

Other signs point to a dysfunctional Pentagon on Mr. Hegseth’s watch.

Last week, the Defense Department removed an online article about the military background of Jackie Robinson, who became the first African American to play in Major League Baseball in 1947, after serving in the Army.

The article — which reappeared after a furor — was one in a series of government web pages on Black figures that have vanished under the Trump administration’s efforts to purge government websites of references to diversity and inclusion.

In response to questions about the article, John Ullyot, a Pentagon spokesman, said in a statement that “D.E.I. is dead at the Defense Department,” referring to diversity, equity and inclusion efforts. He added that he was pleased with the department’s “rapid compliance” with a directive ordering that diversity-related content be removed from all platforms.

Mr. Ullyot was removed from his position shortly afterward.

Sean Parnell, the chief Pentagon spokesman, said in a video that the screening of Defense Department content for “D.E.I. content” was “an incredibly important undertaking,” but he acknowledged mistakes were made.

The Pentagon leadership under Mr. Trump expressed its disdain for the military’s decades-long efforts to diversify its ranks. Last month, Mr. Hegseth said that the “single dumbest phrase in military history is ‘our diversity is our strength.’”

Mr. Hegseth also came under sharp critique from the federal judge handling a lawsuit against his efforts to ban transgender troops. “The military ban is soaked in animus and dripping with pretext,” Judge Ana C. Reyes of U.S. District Court in Washington wrote in a scathing ruling last week.

“Its language is unabashedly demeaning, its policy stigmatizes transgender persons as inherently unfit and its conclusions bear no relation to fact,” she wrote in her decision temporarily blocking the ban. “Seriously? These were not off-the-cuff remarks at a cocktail party.”

Greg Jaffe contributed reporting.