Investigators believe a Saudi Air Force lieutenant acted alone when he killed three people and wounded eight at a US Navy base in Pensacola, Florida, on Friday, the FBI said on Sunday, according to Reuters.

They have yet to determine a motive for the rampage, even though fellow Saudi students at the base who were close to the shooter are cooperating with investigators, said Rachel Rojas, special agent in charge of the FBI’s Jacksonville office and lead investigator on the case.

Rojas said the FBI was working, as it does in most mass shootings, on the presumption that it was an act of terrorism, but stressed that was largely to allow investigators to use special tools afforded to them in terrorism cases.

“We are looking very hard at uncovering his motive and I would ask for patience so we can get this right,” she said, according to Reuters, adding that 80 FBI special agents, 100 support staff and scores of other investigators from the Navy and multiple federal agencies were working the case.

The FBI has identified the shooter as Second Lieutenant Mohammed Saeed Alshamrani, 21.

Rojas said the pistol he used - a Glock 9mm handgun that can be paired with a magazine holding 33 rounds - was legally purchased by the shooter somewhere in Florida.

Alshamrani was on the base as part of a US Navy training program designed to foster links with foreign allies.

His fellow Saudi students were speaking directly to American investigators and were restricted to the base on order of the Saudi military, Rojas said.

A group that tracks online extremism has said Alshamrani appeared to have posted criticism of US wars in predominantly Muslim countries and quoted former Al-Qaeda leader Osama bin Laden on Twitter hours before the shooting spree.

In English, he also wrote that he hated the American people for “committing crimes not only against Muslims but also humanity,” and he criticized Washington’s support for Israel, according to analysis by the SITE Intelligence Group.