The FBI believes a Saudi Air Force lieutenant acted alone in a possible act of terrorism when he killed three people and wounded eight at a US Navy base in Pensacola, Florida, before being fatally shot by a deputy sheriff.
They have yet to determine a motive for the rampage but the FBI is working, as it does in most mass shootings, on the presumption that it was an act of terrorism.
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 stressed that the presumption of terrorism 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, 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 identified the shooter as Second Lieutenant Mohammed Saeed Alshamrani, 21, and said he opened fire inside a classroom at the base early on Friday morning.
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.
According to US regulations, it is legal for a foreigner in the United States on a non-immigrant visa to buy a gun if certain conditions are met - including if they simply have a hunting licence.
Alshamrani was on the base as part of a US Navy training program designed to foster links with foreign allies. He had been in the Pensacola area for the past 18 months.
US President Donald Trump said on Saturday that King Salman and Crown Prince Mohammed bin Salman were "devastated" by what took place and pledged to help families of the victims.
The Saudi crown prince called Trump on Sunday to assure him Saudi authorities would offer their absolute cooperation with the United States and provide all information that would help the investigations, the Saudi state news agency reported.
But members of Congress representing Florida have blasted the US government for not already labelling the shooting as a terrorist attack and have demanded more details about what the Saudi government is doing to help the investigation and prevent future violence by members of its military.
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.
In English, he also wrote that he hated the American people for "committing crimes not only against Muslims but also humanity," and he criticised Washington's support for Israel, according to analysis by the SITE Intelligence Group.
Florida Governor Ron DeSantis answered "yes, yes" on Sunday when asked if he considered the shooting an act of terrorism.
"You have foreign military personnel coming to our base. They should not be doing that if they hate our country."
DeSantis said Alshamrani took advantage of a "federal loophole" to buy the gun he used.
US Defence Secretary Mark Esper said he had asked the Pentagon to review screening procedures for military personnel from other countries coming to the United States for training.
Australian Associated Press