The FBI has said US investigators believe Saudi Air Force Second Lieutenant Mohammed Saeed Alshamrani, 21, acted alone when he attacked a US Navy base in Pensacola, Florida on Friday, before he was fatally shot by a deputy sheriff.

The shootings have again raised questions about the US military relationship with Saudi Arabia, which has come under heightened scrutiny in Congress over the war in Yemen and Saudi Arabia's killing of Washington Post columnist Jamal Khashoggi last year.

Still, US military leaders have sought to portray this as a localised issue which would not affect the overall US-Saudi relationship.

"A safety stand-down and operational pause commenced Monday for Saudi Arabian aviation students," navy spokeswoman Lieutenant Andriana Genualdi told Reuters on Tuesday.

Another US official said the grounding was to help Saudi students prepare to eventually restart their training and similar procedures would have been taken if such an incident took place in a US military squadron.

An Air Force spokeswoman told Reuters an undisclosed number of additional Saudi students have also stopped flying.

"Given the traumatic events, we feel it is best to keep the Royal Saudi Air Force students off the flying schedule for a short time," the spokeswoman said.

"We are ensuring our Saudi students have access to available resources to help them deal with these circumstances. The safety and well-being of all our aircrew is a top priority."

Genualdi said the grounding included three different military facilities: Naval Air Station Pensacola, Naval Air Station Whiting Field and Naval Air Station Mayport, all in Florida.

She added that while it was unclear when the Saudi students would be allowed to fly again, their classroom training was expected to resume soon, however, she said aviation training had resumed for students from other countries.

There are currently about 850 Saudi students in the United States for military training.

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

He had started training in the United States in 2017 and had been in the Pensacola area for the past 18 months, authorities said.

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

The attack comes as President Donald Trump's administration has maintained warm ties with Riyadh amid high tensions with Middle East rival Iran.

US Defense Secretary Mark Esper has dismissed suggestions that the shootings might make him more reluctant about new US deployments to Saudi Arabia, which were announced in October.

Australian Associated Press