Military officials have directed recruiting and reserve centers in the United States to tighten security after deadly attacks in Chattanooga, Tennessee, last week that killed four Marines and a sailor.

The directive from U.S. Northern Command, which oversees homeland security efforts for the Defense Department, also applies to Reserve Officer Training Corps units, spokeswoman Army Maj. Beth Smith said on Monday.

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She would not specify what the additional security measures would be, but noted that "we increased our vigilance." Northern Command chief Adm. Bill Gortney in May had already ordered a boost in security at military bases nationwide to the highest level since the 9/11 attacks.

Defense Secretary Ash Carter, meanwhile, has ordered a security review of military facilities.

The gunman in Thursday's attack, Mohammad Youssuf Abdelazeez, 24, of Hixson, Tenn., was killed by police when he opened fire on them. Federal authorities are investigating his connections to Islamist extremist groups, including the Islamic State, though a family statement said he was depressed and also had been taking drugs.

In the wake of the attacks, some state governors have ordered National Guard troops, which operate under state control via Title 32 of the U.S. Code, to carry arms at domestic facilities. Smith would say only that local commanders may take additional security measures they think are appropriate when asked if recruiters and reservists — who are under the federal government's control — will follow suit.

"They have the leeway to implement additional security measures as they see fit," she said.