In the call with President Donald Trump, the king expressed "deep sorrow" over the Florida shooting and pledged cooperation with American officials, the official Saudi Press Agency said.

"He (the king) affirmed that the perpetrator of this heinous crime does not represent the Saudi people," it reported.

Three people were killed and eight others wounded in the incident, according to US authorities.

The Saudi king "assured Trump of the kingdom's full support to the United States, as he ordered Saudi security services to cooperate with American agencies to uncover information that will help uncover the circumstances behind this unfortunate incident," the SPA reported.

The shooting took place in a classroom building at Naval Air Station Pensacola in Florida.

Florida Governor Ron DeSantis said the shooter, who was gunned down by police, was part of the Saudi air force.

Saudi Arabia's de facto ruler Crown Prince Mohammed bin Salman, seeking to modernise the ultra-conservative Islamic kingdom, has sought to shrug off its longstanding reputation as an exporter of terrorism ideology.

Fifteen of the 19 men involved in the September 11, 2001 attacks were Saudi nationals, some of whom attended flight school in Florida.