Story highlights A Navy official said that so far only one or two civilian armed guards have shown up at recruiting centers.

Defense Secretary Ashton Carter has asked for a Pentagon review recommending how to improve security at military installations.

Washington (CNN) A Navy official tried to throw more cold water Wednesday on armed private citizens showing up on their own at military recruitment centers.

The official told CNN that should unauthorized armed civilians attempt to patrol outside a Navy recruiting center, recruitment personnel would try to work out of the office. They could choose to spend the day at a school, mall, on travel or other duties that would keep them away from the center.

The official noted, however, that so far only one or two of these armed civilians have shown up following the shooting at a Chattanooga, Tennessee, recruiting center Thursday that left five servicemen dead.

Earlier Wednesday, Department of Defense spokesman Capt. Jeff Davis reiterated the existing department policy of not supporting arming all military personnel in comments to reporters.

Lawmakers and elected officials at the national, state and local levels have proposed changing the policy following the deadly shooting Thursday.

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