MIAMI — The Pentagon has suspended operational training for all Saudi military students in the United States, indefinitely halting flight instruction, firing range training and all other operations outside the classroom in the wake of a shooting last week at Naval Air Station Pensacola by a member of the Saudi Royal Air Force.

The suspension will affect nearly 900 Saudi students across the country, the Defense Department said on Tuesday. Classroom teaching, including language courses, will continue while Pentagon leaders review vetting procedures for all foreign military trainees. An estimated 5,100 international students in the United States will be covered by the security review.

The “safety stand-down” was issued pending the results of an F.B.I. investigation into the shooting on Friday that left three young sailors dead and eight other people wounded. Several lawmakers, including Senator Rick Scott of Florida and Representative Matt Gaetz, whose congressional district includes Pensacola, had called for a review of foreign military programs and their screening process.

Defense Secretary Mark T. Esper discussed the decision on Tuesday with his Saudi counterpart, according to the Pentagon.

The Navy had announced earlier on Tuesday that about 300 Saudi aviation students would be grounded at three bases in Florida. The Pentagon later released a memo from David L. Norquist, the deputy secretary of defense, clarifying that the suspension would apply to 852 Saudis enrolled in all military training programs.

The memo described Saudi Arabia an “essential partner” that is working closely with the United States to investigate the shooting.

“The Department has trained more than 28,000 Saudi students over the life of our security cooperation relationship without serious incident,” Mr. Norquist wrote.

He gave military staff members 10 days to complete a review of policies for vetting foreign students and granting access to American military bases, though the Saudi operational suspension will likely last longer.

He said the leadership of the various branches of military service “may take additional security measures as they see fit.”

All flight training at Pensacola had been suspended over the weekend after Friday’s attack. Some training was allowed to resume on Monday, though not for Saudi students, who have been restricted to the base since the shooting.

The students received a visit late on Monday from Saudi Arabia’s defense attaché, according to the F.B.I.

The latest orders came as investigators released new details about how the 21-year-old gunman, Mohammed Saeed Alshamrani, had acquired the weapon used in the shooting.

The gunman legally purchased the Glock 45 9-millimeter handgun in late July, shortly after he had obtained a state hunting license, the F.B.I. said on Tuesday.

Mr. Alshamrani was issued a hunting license on July 11, according to the Florida Fish and Wildlife Conservation Commission. Nine days later, on July 20, he purchased the handgun at a federally licensed firearms dealer in Florida.

The ability for a foreign military student to legally buy a gun has come under scrutiny after Friday’s attack. The gunman used an extended magazine and had four to six other magazines in his possession when he was killed by a sheriff’s deputy, a person familiar with the investigation has said.

Those who travel to the United States on a nonimmigrant visa, as the gunman did, are prohibited under federal law from having a weapon or ammunition. But the law also lists several exceptions, including one for those holding a valid hunting license.

Mr. Alshamrani may have qualified to legally buy a gun under other exceptions as well, according to the F.B.I.’s Jacksonville field office, which is leading the investigation.

Other exceptions are included in the law for accredited representatives of foreign governments, distinguished foreign visitors designated by the State Department, or foreign law enforcement officers of a friendly government entering the United States on official business.

Gov. Ron DeSantis, a Republican, called the exceptions a “loophole” in federal gun laws that should be closed.

“I’m a big supporter of the Second Amendment, but the Second Amendment applies so that we the American people can keep and bear arms,” Mr. DeSantis, a former Navy prosecutor, said at a Sunday news conference in Pensacola. “But it does not apply to Saudi Arabians.”

Much remains unknown about the gunman and his motive, though the F.B.I. is treating the shooting as a presumed act of terrorism. Investigators have received information that Mr. Alshamrani was active on social media. Though they have not released any specifics, the SITE Intelligence Group, which monitors jihadist activity online, found a Twitter account with a name matching the gunman’s criticizing the United States as “evil.”

The Pentagon heightened security reviews at bases around the country on Monday, citing the two shootings that occurred last week on military bases, in Pensacola and at the Pearl Harbor Naval Shipyard in Hawaii. In the Pearl Harbor attack, the gunman fatally shot two shipyard workers before killing himself.

On Tuesday, Thomas B. Modly, the acting Navy Secretary, awarded posthumous “wings of gold” to the three Pensacola victims, proclaiming Ensign Joshua Kaleb Watson a naval aviator and Airman Mohammed Haitham and Airman Apprentice Cameron Walters naval aircrewmen. Five of the injured had been sent home from the hospital by Monday, with the three remaining patients in stable condition.

Mr. Alshamrani first arrived in the United States in August 2017 for a year of English-language training at Lackland Air Force Base in San Antonio, according to a Pentagon official. He later spent a year and a half in aviation training in Pensacola, before moving on to advanced strike fighter training in October.

In April, Mr. Alshamrani filed a formal complaint against one of his instructors at the base whom he accused of embarrassing him in front of other aviation students by mocking his mustache as looking like that of a pornographic actor.

The F.B.I. did not identify the shop where Mr. Alshamrani bought the gun, but ABC News reported it was Uber’s Lock and Gun in Pensacola. Naomi Uber, the owner, declined to comment on Monday, referring questions about the gun purchase to the federal Bureau of Alcohol, Tobacco, Firearms and Explosives, which in turn directed inquiries to the F.B.I.

“There is an ongoing investigation,” Ms. Uber said. “I can’t pull up paperwork. I don’t have authority to discuss anything with you.”

Kenny Lewis, who runs guided hunting tours in the Florida Panhandle, scoffed at the idea of hunting with a Glock 45 handgun. It is not unheard-of, he said: A handful of hunters have shown up for trips in recent years with similar handguns, but they were mostly novice hunters. Sometimes, he said, hunters carried them out of fear of being attacked by a wild hog.

Mr. Lewis said most hunters prefer a rifle that can do more damage and has a longer range, even if it means firing at a slower rate.

“A Glock 45 is more purchased for self-defense, for creating harm to someone else or for target shooters,” Mr. Lewis said, “especially with an extended clip.”

Patricia Mazzei reported from Miami, and Eric Schmitt from Washington. Nicholas Bogel-Burroughs contributed reporting from New York and Frances Robles from Pensacola, Fla.