Tennessee Highway Patrol officers and the Chattanooga Police Department on Sunday escort a hearse carrying the body of U.S. Navy Petty Officer 2nd Class Randall Smith, who died Saturday after Thursday’s shooting in Chattanooga. (John Rawlston/AP)

— The FBI has recovered a pistol that may have been privately owned and used by one of the Marines killed here Thursday during the shooting at the Navy Operational Support Center, according to law enforcement officials.

Investigators are trying to determine, based on forensics, whether the pistol, a 9mm Glock, was used in an exchange with the shooter, Mohammad Youssef Abdulazeez, and possibly wounded him, officials said.

The standard-issue pistol for military personnel authorized to carry a sidearm is a variant of the 9mm Beretta 92. According to the Marine unit’s commanding officer, Maj. Mike Abrams, Marines are not authorized to carry personally owned firearms while at the support center.

An FBI spokesman declined to comment.

The shooting has prompted calls to arm military personnel at bases and other facilities, including recruiting centers, in the United States. In the 1990s, the Pentagon restricted who can carry weapons at domestic military facilities, ostensibly to make them safer by allowing only military police to carry weapons in most situations.

Sen. John McCain (R-Ariz.), chairman of the Senate Armed Services Committee, and Rep. Mac Thornberry (R-Tex.), chairman of the House Armed Services Committee, called Friday for the Pentagon to do more to protect troops.

“Long before the Chattanooga attack, we had been working to clarify a post commander’s authority to allow carrying of personal firearms,” McCain and Thornberry said in a joint statement. “This year’s National Defense Authorization Act will reflect that work. Together, we will direct the Pentagon to end the disconnect between the threats our war fighters and their families face and the tools they have to defend themselves.”

Law enforcement officials said they were still sifting through details of Abdulazeez’s life and trying to figure out what specifically led to shootings. Abdulazeez, whose family said he had been suffering from depression, did not have an extensive social-media profile, officials said.

A family representative said Monday that the FBI also recovered personal writings from his house that were depressive and contained extremist views, including references to martyrdom. The notes did not appear to be written recently.

Four Marines were killed Thursday when Abdulazeez, after ramming his rented Ford Mustang through a gate, headed into the reserve center and began firing. Navy Petty Officer 2nd Class Randall Smith, the fifth service member killed in the attack, died from his wounds early Saturday.

Before entering the reserve center, Abdulazeez had fired more than 50 rounds into a recruiting office 15 minutes away on the other side of town. No one was injured in that exchange — most likely because of the office’s recently installed bulletproof windows.

Although Abrams said he was unable to comment precisely about the events of the day because of the ongoing investigation, he was quick to point out that the Marines were anything but helpless as Abdulazeez advanced.

“They acted very quickly. They hunkered down and protected one another,” said Abrams, who took command of the artillery unit Mike Battery, 3rd Battalion, 14th Marines, in 2013. “The Marines acted with valor that day. There was some heroic actions that had an impact on the events.”

After Abdulazeez was killed, most likely by law enforcement officers who arrived on the scene, investigators found that he had a Kalashnikov variant rifle, a Smith & Wesson handgun and a Saiga-12 semiautomatic shotgun. The Glock was apparently found near one of the dead Marines.

Abdulazeez had also purchased an AR-15 semiautomatic assault rifle that was recovered at the family’s home, officials said.

His family is awaiting the results of an autopsy that is expected to confirm how he died.

“It was clear that this gunman had every intent to encounter and to murder police officers if he needed to,” Chattanooga Police Chief Fred Fletcher said at a Friday news conference.

During the shootout with police, Abdulazeez shot one of the Chattanooga police officers. The officer, who was struck in the ankle, had to be dragged to cover while his colleagues continued to return fire.

Dan Lamothe contributed to this report.