The FBI says it is treating Friday’s deadly attack on a Florida navy base as a presumed terrorist attack.
The Saudi gunman – who was training at the Pensacola site – killed three sailors before he was shot dead.
Special agent Rachel Rojas said the FBI was trying to determine if he had acted alone or had connections to a group.
She said other Saudi students had been questioned but not arrested. They were reportedly confined to the base and co-operating with investigators.
The victims of the attack have been named as Joshua Kaleb Watson, 23, Mohammed Sameh Haitham, 19, and Cameron Scott Walters, 21.
In Sunday’s press conference, Ms Rojas gave almost no details of the investigation’s findings so far.
However, she did say that the gunman, 21-year-old Mohammed Alshamrani, bought his weapon legally in the US. It was a 9mm handgun.
It has been reported in US media that Alshamrani played mass-shooting videos to others at a dinner earlier in the week, according to an anonymous official briefed on the investigation.
A Twitter user appearing to match Alshamrani’s identity also made a series of anti-US posts before the shooting, an online monitoring group says.
Alshamrani had also filed a formal complaint against one of his instructors over a nickname which he said had humiliated him.
Alshamrani alleged the instructor had called him “Porn Stash”, an apparent reference to the moustache of a porn actor, in front of 10 other aviation students in April.
“I was infuriated as to why he would say that in front of the class,” Alshamrani wrote in the complaint, the New York Times reported.
At a separate press conference on Sunday, Florida Governor Ron DeSantis said the gunman had “a major social media trail” and called for more stringent security measures.
“This guy was somebody who just had a deep-seated hatred for the United States and that was pretty clear from that,” he said.
“My view is that… for us to be bringing in these foreign nationals, you have to take precautions to protect the country.”
The Pensacola base has long offered aviation training to foreign military forces.
Saudi pilots started training there in 1995, alongside other personnel from Italy, Singapore and Germany. -BBC