The gunman - Saudi national Mohammed Saeed Alshamrani who was a trainee at the site - killed three people in a classroom before being shot dead.
Authorities have not said the other students were involved.
A Twitter user appearing to match Alshamrani's identity had made a series of anti-US posts, US media say.
But US Defence Secretary Mark Esper said on Saturday that he would not label the incident as "terrorism" at this point.
Speaking at the Reagan National Defense Forum in California, he said investigators must be allowed to do their work first.
The Florida attack was the second shooting to take place at a US military base last week. Two days earlier, a US sailor shot dead two workers at the Pearl Harbor military base in Hawaii.
What happened on Friday?
Authorities were alerted to the shooting at the Pensacola base at 06:51 (12:51 GMT).
It took place across two floors of a classroom building and ended when a sheriff's deputy killed Alshamrani.
Eight people were also injured in the shooting, including two officers, who are expected to recover.
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