Saudi Arabia is a key U.S. ally in the Middle East and President Donald Trump said that the Saudi king called him after the attack to "express his honest condolences and give his sympathies to the families and friends of the warriors who were killed".
The official who spoke to AP said one of the three students who attended the dinner party at the base, hosted by the attacker, recorded video outside the classroom building while the shooting was taking place.
Alshamrani, a 21-year-old second lieutenant in the Saudi Royal Air Force, opened fire in a classroom at the base on Friday, killing three sailors and wounding eight other people before being shot dead by police.
A sheriff's deputy fatally shot the gunman, authorities said, ending the second deadly attack at a USA military base within a week.
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.
The Pentagon should temporarily suspend training for foreign fighters, Republican lawmakers, including Representative Matt Gaetz and Senator Lindsey Graham, said on Sunday political talk shows.
No terror group immediately claimed the deadly attack carried out by a Saudi military trainee at Naval Air Station Pensacola in Florida.
Graham of SC called for a halt during the investigation of the Florida incident. Saudi Arabia's an ally, but there's something really bad here fundamentally. "We never thought he would die in Florida", his father said. But he also criticised President Donald Trump for not being more aggressive with the kingdom.
Rojas declined to comment on the shooter's travels or activities while based in Pensacola.
The kingdom is still trying to recover from the killing previous year of Washington Post columnist Jamal Khashoggi at the Saudi Consulate in Istanbul.
Rojas added that this presumption was made to speed up the investigation, and help "identify and eliminate" any potential threats to the community if terrorism was indeed the killer's motivation.
During an appearance on the CBS program "Face the Nation" on Sunday, White House national security adviser Robert O'Brien said that at a shooting at a naval base in Pensacola, Fla. on Friday "appears to be a terrorist attack".
"This is a guy who may very well have said some things on Twitter that suggest he was radicalized", O'Brien said. "So, my point is it looks like terrorism".
There are now more than 850 Saudis in the USA for various training activities - among about 5,000 foreigners from 153 countries in the country undergoing some form of military training.
Reports on Saturday said authorities had accounted for 10 Saudi students at Pensacola base and the whereabouts of several others were unknown. Some of the Saudis took cellphone video at the scene, Esper said.
He said it was unclear if they began filming before the shooting began or after it started. "That may be a distinction with or without a difference".
Speaking at the Reagan National Defense Forum in California, he said investigators must be allowed to do their work first. "I was given every assurance from the ambassador that that would occur". "You have foreign military personnel coming to our base".
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