The FBI identified the shooter as 21-year-old Mohammed Alshamrani, 21, a 2nd lieutenant in the Royal Saudi Air Force and a visiting student at the base's Naval Aviation Schools Command. The base was the scene of a massive law enforcement response on Friday, when Alshamrani shot and killed three people, and injured eight, including responders.
The shooting was the second at a USA naval base in a week.
Alshamrani used a Glock 45 9-millimetre handgun that was lawfully purchased in Florida, Rojas said.
Rojas declined to speak to many specifics, including reports that other Saudi nationals filmed Friday's shooting, and that al-Shamrani hosted a dinner party the night before the attack at which he showed videos of previous mass shootings.
A Saudi commanding officer has ordered all students from the country to remain at one location at the base, officials also said at the news conference.
No arrests have been made, Rojas said. Two Saudi students watched from a auto, the official said.
The official said 10 Saudi students were being held on the base on Saturday while several others were unaccounted for.
"A large number of Saudi graduates of the Naval Air Station in Pensacola moved on to serve with their United States counterparts in battlefronts around the world, helping to safeguard the regional and global security".
Earlier on Saturday, a United States official told CNN that a number of Saudi nationals have been detained for questioning in connection with the shooting. "Bringing in people from Saudi Arabia - we need to be on guard against that".
The lawmaker said the ambassador assured him that full cooperation would be provided.
O'Brien spoke on CBS' "Face the Nation".
"This has been done for many decades", Trump said. They think Romero acted alone and that there was no indication he was a domestic terrorist.
President Donald Trump told reporters on December 7 that he had spoken with the king of Saudi Arabia and Crown Prince Mohammad bin Salman about the shooting.
But Representative Matt Gaetz, a Republican whose Florida district includes the Pensacola base, warned the shooting "has to inform on our ongoing relationship with Saudi Arabia".
Authorities detained several of the shooter's friends after the killing.
Why were Saudis at the USA base?
Donald Trump also indicated a review of policies governing foreign military training.
Lawrence Keefe, U.S. Attorney for the Northern District of Florida, said that he would be comfortable for any member of his family to be out in public.
The FBI's Ms. Rojas told reporters that "there are a number of Saudi students who are close to the shooter and continue to cooperate in this investigation".
He referred to United States wars in Muslim countries, writing that he hated the American people for "committing crimes not only against Muslims but also humanity", and criticizing Washington's support for Israel, SITE's analysis said.
Citing a person briefed on the investigation, the New York Times reported that friends and colleagues thought the gunman, a Muslim, had become more religious after returning to the USA this February.
Killed in the rampage were Ensign Joshua Kaleb Watson, 23, from Coffee, Alabama; Airman Mohammed Sameh Haitham, 19, from St. Petersburg, Florida; and Airman Apprentice Cameron Scott Walters, 21, from Richmond Hill, Georgia.