CBS News has learned the gunman's name was Mohammed Saeed Alshamrani, a Saudi Arabian national and a pilot-in-training for the Saudi Air Force. He had been training in the United States since 2017.
The FBI is investigating Alshamrani's social media posts and whether he acted alone. According to the Middle East Media Research Institute, a nonprofit based in Washington, D.C., someone matching Alshamrani's identity had an extensive online footprint.
In a Twitter post, the writer says, "O American people, I'm not against you for being American, I don't hate you because your freedoms, I hate you because every day you supporting, funding and committing crimes not only against Muslims but also humanity."
Investigators are looking for any signs of radicalization going back to Alshamrani's upbringing in Saudi Arabia.
Investigators are not saying if the shooting was an act of terror. They have not stated a possible motive.
"We are not prepared at this hour to confirm what may have motivated the shooter to commit this horrific act today," Rachel Rojas, special agent in charge of the FBI Jacksonville Division, said Friday.
The sprawling naval base was locked down on Friday after Alshamrani – one of a few hundred foreign nationals training at the Naval Air Station Pensacola – stormed a classroom and opened fire with a handgun.
The FBI is trying to determine how a foreign national obtained a handgun, which is prohibited by law, and brought it onto the base.
Defense Secretary Mark Esper said Friday he'll look at the vetting measures that go into accepting foreign nationals to be able to train.
Saudi King Salman called President Donald Trump after the shooting.
"The King said that the Saudi people are greatly angered by the barbaric actions of the shooter, and that this person in no way shape or form represents the feelings of the Saudi people who love the American people," the president said on Friday.