The Defense Department has completed security screenings of all Saudi Arabian students in the U.S. for military training and found no indications of any immediate threats, the Pentagon said Thursday, nearly two weeks after a Saudi student killed three people and injured eight others at a Florida Navy base.

Garry Reid, the director for defense intelligence, told reporters that as a result of an ongoing security review, the Pentagon will expand its role in vetting international students who come into the country for military training. He added that the department will now conduct additional vetting of all other international students who are in the U.S. for military programs.

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On Dec. 6, 2nd Lt. Mohammed Alshamrani, a 21-year-old Saudi Air Force officer, killed three U.S. sailors and injured eight other people at Naval Air Station Pensacola. Federal authorities say he legally bought the 9mm Glock pistol he used.

The incident raised questions about how well international military students are screened before they attend training at American bases.

As a result, the Pentagon last week ordered a broad review of the screening procedures. In a Dec. 10 memo, Deputy Defense Secretary David Norquist also ordered the suspension of all flight and other operational training for Saudi Arabian students in U.S. military programs.

In addition, the Pentagon also said that no new international military students would come into the United States for training until new screening procedures are in place.

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A senior U.S. defense official said Thursday that although the latest screening indicated no threat from Saudi students in the U.S., that doesn't reflect any other information that federal investigators may be gathering about what role any other individuals may have played in the Pensacola shooting. The official, who spoke on condition of anonymity to discuss an ongoing investigation, also said that military bases have instituted other enhanced security procedures, including more random searches and perimeter checks.

The Pentagon has said that about 850 Saudi students are currently in U.S. military training programs. Officials said it's not certain when flight and operational training would restart.

Overall there are about 5,000 international military students in U.S. programs. Currently, they go through screening by the State Department and the Department of Homeland Security. The U.S. mainly runs background and biometric checks on the students to determine if they are security risks.

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For the most part, military installation commanders have the authority to set their own security procedures, including base entry screenings and carry permits for guns. There is a baseline level of security that must be met, but commanders can make any of their procedures more stringent if they believe it's necessary.