Addressing the media on Sunday, Special Agent Rachel Rojas said the FBI was trying to determine if the Saudi gunman, identified as Mohammed Alshamrani (21), had acted alone or had connections to a group, the BBC reported.
She said that other Saudi students had been questioned at the Pensacola base but not arrested.
They were reportedly confined to the base and co-operating with investigators.
Rojas added that Alshamrani bought his weapon, a 9mm handgun, legally in the US.
The victims of the attack have been named as Joshua Kaleb Watson (23), Mohammed Sameh Haitham (19), and Cameron Scott Walters (21).
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," the BBC quoted DeSantis as saying.
"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.
Currently, about 200 international students were enrolled in programmes at the base. According to its website, the base employs more than 16,000 military and 7,400 civilian personnel.
Alshamrani was a second lieutenant in the Saudi Air Force.
( With inputs from IANS )