Defense Secretary Pete Hegseth had what he thought was a good idea. A man convicted of going on a shooting rampage at a Texas Army base in 2009 had been sitting in a federal prison on death row for more than a decade, his execution on hold until a U.S. president signed off. Lethal injection drugs weren’t widely available, and Hegseth recommended to President Trump another option—death by firing squad.

Trump approved the plan, but White House and Pentagon officials said they were surprised days later when Hegseth announced a twist: The firing squad execution would be “public,” the defense secretary told conservative activist Jack Posobiec in an on-camera interview, “because people need to understand that there is serious consequences for these types of things.”The Pentagon later confirmed his intention was to livestream the execution.

The announcement stunned White House and Pentagon aides, triggering a dayslong internal debate on whether such a bloody spectacle broadcast to the public would be a good idea, according to people familiar with the discussion.

Trump told reporters and allies that he wasn’t involved in the initial decision to broadcast the execution. Privately, Trump said he wasn’t aware that the man convicted in the shooting, Maj. Nidal Hasan, had been paralyzed in the attack and used a wheelchair, the people said. Trump didn’t like the optics of U.S. military officers shooting a man in a chair to death on live TV, they said.

Also skeptical that broadcasting the execution would serve as a kind of deterrence, Trump began privately asking individual advisers what they thought, one person said.

Vice President JD Vance and House Speaker Johnson had publicly questioned the idea, insisting they had no intention of watching a public execution.

A week later, Trump called off the livestream. In a statement, the White House pointed reporters to Trump’s social-media post that streaming the execution “may have been a strong deterrent for the world to witness how America deals with terrorists,” but that “many good and well-meaning people would rather not watch him die.”The Pentagon said Hegseth and Trump spoke about the decision not to livestream Hasan’s execution before the president announced that he would be walking back Hegseth’s plan.

“The Secretary supports the President’s decision, and they are completely aligned,” said chief Pentagon spokesman Sean Parnell.

Hasan, a U.S.-born Muslim, was working as an Army psychiatrist at Fort Hood Army base in Texas when he opened fire, killing 13 and wounding dozens more in what is considered one of the worst soldier-on-soldier crimes in U.S. military history. He later admitted to the killings, saying he was trying to defend fellow Muslims. By 2013, he was sentenced to the death penalty.

As Hasan languished on death row in a military prison at Fort Leavenworth, Kan. Pentagon officials were planning an execution by lethal injection subject to presidential approval. But the drug cocktail had become more difficult to acquire, and Army officials discovered earlier this year that it would take several months to obtain the dose intended for Hasan.

Hegseth then recommended that Hasan face a firing squad, which Trump approved on Oct. 2, the Pentagon said.

The following week, Hegseth was giving a televised interview aboard the USS Abraham Lincoln aircraft carrier with Posobiec, a conservative activist, when he said executing Hasan by firing squad was a “no-brainer.”He said the planned execution would take place Dec. 3 and that it would be made public.

The remarks immediately set off a scramble on both sides of the Potomac as Pentagon officials began reworking long-laid plans for Hasan’s execution. The military hasn’t killed someone by firing squad since World War II, and officials were grappling with a series of new legal and practical decisions.

The number of witnesses to federal and state executions is tightly controlled. Under existing Army regulation, no one under the age of 18 is allowed to witness an execution of a U.S. servicemember, a rule that would be impossible to enforce if the execution were livestreamed on the internet.

Then there was the challenge of transporting Hasan, who is being held in a maximum-security prison, to Fort Hood for the event, and what type of ammunition to use for the execution, according to Pentagon officials.

Hegseth’s comments also set off an internal White House debate that spilled into the open a day later when Vance told reporters he was skeptical the execution would be livestreamed.

“I don’t know that’s actually going to happen,” Vance told reporters the day after Hegseth’s announcement. “Let’s sort of see what—I think it’s going to happen in December when he’s executed.”House Speaker Mike Johnson (R., La.) told CBS News that there were concerns that footage of the execution would become a “recruiting tool for future terrorists,” while congressional Republicans weighed in with rare public statements against the idea.

“Secretary Hegseth should seriously reconsider this decision,” said Rep. Tom Barrett (R., Mich.), a former Army officer who said he trained at Fort Hood the year before the attack.

“Making a public spectacle out of an already tragic situation is unnecessary and does not serve a public interest,” he added.

This week, tens of thousands of Army officers, defense industry representatives and foreign military officials arrived in Washington for the Army’s largest annual exposition, held at the Convention Center. Attendees furtively discussed the livestream while listening to speeches in the ballroom and watching live equipment demonstrations on the exposition floor.

When asked how the livestream would take place, acting Army Secretary Adam Telle said in a brief interview: “I think we’re planning all that out.”By Thursday, nationwide polling showed 8 in 10 Americans opposed the livestreaming idea, although a majority backed putting Hasan to death by firing squad.

Later that day, Trump announced that he was reversing Hegseth’s decision, writing on social media that the execution wouldn’t be livestreamed.

“He will die, as scheduled, by firing squad, but this event will not be streamed,” Trump wrote. “That said, the execution may be viewed in person by the immediate families of the victims, if they so choose.”

Write to Lara Seligman at lara.seligman@wsj.com, Alex Leary at alex.leary@wsj.com and Philip Wegmann at philip.wegmann@wsj.com