"We are looking very hard at uncovering his motive and I would ask for patience so we can get this right", she said.
Investigators also believe the gunman visited New York City, including Rockefeller Center, days before the shooting and are working to determine the objective of the trip, said the official, who was not authorized to discuss the matter publicly and spoke to the AP on condition of anonymity.
Speaking at the Reagan National Defense Forum in California, he said investigators must be allowed to do their work first.
Alshamrani opened fire in a classroom building on Friday. Sheriff's deputies shot the gunman dead.
The FBI identified Alshamrani as the shooter.
"The sorrow from the tragic event on NAS Pensacola will have a lasting impact on our installation and community", Captain Tim Kinsella, the commanding officer of the naval base said in a statement.
It does not appear he had ties to terrorist groups, two sources told CNN.
Air Force Gen. Terrence O'Shaughnessy, who oversees U.S. base security as chief of U.S. Northern Command, has directed domestic bases and units to "immediately assess force protection measures and implement increased random security measures for their facilities", Northcom said in a tweet early Sunday morning.
Officials at the Navy base referred questions to the Federal Bureau of Investigation, which also did not comment.
The younger Alshamrani appeared to have posted a justification of his planned attack in English on Twitter a few hours before it began, according to SITE Intelligence Group, which monitors online Islamist extremism. A federal law enforcement official said they are working to determine the objective of his trip to NY.
They visited several museums and Rockefeller Center, where the Christmas tree lighting was taking place.
"I wish the president was pressing the Saudi government for answers", he said.
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The Saudis who accompanied Alshamrani are now being interviewed by law enforcement and are being cooperative, the source added.
News reports other Saudi students had been questioned but not arrested.
Joshua Watson had just graduated from the U.S. Naval Academy and looked forward to a military career as a pilot.
"The King said that the Saudi people are greatly angered by the barbaric actions of the shooter, and that this person in no way shape or form represents the feelings of the Saudi people who love the American people", Trump added.
"Number one, we need to suspend the program until we investigate".
O'Brien's remarks were in contrast with those of Secretary of Defense Mark Esper, who on Saturday was careful to emphasize that he did not know if it was a terrorist attack. Alshamrani was being trained in aviation and the English language as part of the program.
On Facebook, his brother Adam Watson wrote: "He died a hero and we are beyond proud but there is a hole in our hearts that can never be filled".
The official said 10 Saudi students were being held on the base on Saturday while several others were unaccounted for.
One deputy, who was shot in the arm, was treated and released on Friday. Both deputies are expected to survive.
Details about the others who were wounded were not available.
These comments came after the U.S. Navy identified the three victims of Friday's shooting.