Six Saudi citizens were arrested near the naval base of Pensacola, in the northwest of the state of Florida, where there was a shooting that left four dead, including the attacker, according to official sources.
The detainees are being questioned in connection with the shooting on Friday morning at the Pensacola Naval Air Station (NAS), a senior US official quoted by Fox News said.
The shooter, who killed three people before being killed by police officers, was identified as Mohammed Saeed Alshamrani, a student in training and a member of the Saudi army, the official added.
The FBI investigation into the shooting in Pensacola is carried out worldwide, according to a police source, the CNN network reported.
The authorities are in constant communication with the government of Saudi Arabia, as the attacker is of Saudi origin.
U.S. Defense Secretary Mark Esper said his first priority is to support the ongoing investigation and determine the motives of the shooter.
Esper referred to the shooter as a Saudi citizen who was a second lieutenant in flight training.
"I want to make sure that we are doing our due diligence to understand what our procedures are" with respect to the training programs, he added.
The Navy said that the majority of the hundreds of foreign aviation students who have participated in the program are from Saudi Arabia. The naval training program has about 1,500 pilots in total.
The Naval Air Station, which houses some 16,000 soldiers and another 7,000 civilians, is home to the Navy Blue Angels flight demonstration squad and is the first stop for training to become naval pilots or officers of flight.
This shooting in Pensacola occurs two days after two people died and another was wounded at the base of Pearl Harbor, in Hawaii, at the hands of a sailor who opened fire and then killed himself.