President Obama is set to address a major veterans' group on Tuesday under pressure to implement a more effective strategy against attacks on U.S. forces at home by Islamic extremists, including a proposal to let troops carry arms at their bases in the United States.

The controversy was re-opened after Thursday's attack on a military recruiting station and a reserve center in Chattanooga, Tenn., that killed four Marines and a sailor.

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

White House spokesman Josh Earnest said Monday that Obama may address the shooting in his speech to the Veterans of Foreign Wars national convention in Pittsburgh, but he's leaving any changes in policy up to the Pentagon, including the question of whether to arm troops at their domestic bases.

RELATED: New security measures ordered following Chattanooga shootings

"That's a policy decision that should be made by the Department of Defense and I don't know if that's something that they're reconsidering at this point. It's the president's view that that decision should be made with solely the safety and security of our men and women in uniform in mind, and not as the subject of a political argument," Earnest said.

Defense Secretary Ash Carter has ordered a security review of military facilities that's due in the next few days, and U.S. Northern Command, which oversees homeland security efforts for the Pentagon, directed recruiting and reserve centers in the United States to tighten security on Sunday.

The administration has faced questions about its strategy toward dealing with attacks on U.S. troops since the Nov. 5, 2009, shooting at Fort Hood, Texas, in which 13 people died when Army psychiatrist Nidal Hasan opened fire in a processing center for troops preparing to deploy overseas.

Hasan, a U.S.-born Muslim who was sentenced to death after being court-martialed for murder, was described in a February 2011 Senate committee report as a "ticking time bomb" whose Islamic extremist views were known to both Army and FBI officials, who took no action in time to stop him.

Related: Tenn. governor urges Congress to protect military recruiting centers

Since then, many — but not all — the fatal shootings and threatened incidents at military bases have been blamed on Islamic extremists, a trend that has accelerated since the rise of the Islamic State last year.

In May, Northern Command chief Adm. Bill Gortney ordered a boost in security at military bases nationwide to the highest level since the 9/11 attacks, calling such threats the "new normal."

This threat also has sparked calls from congressional lawmakers and governors to allow troops to carry arms.

"Long before the Chattanooga attack, we had been working to clarify a post commander's authority to allow carrying of personal firearms. This year's National Defense Authorization Act will reflect that work. Together, we will direct the Pentagon to end the disconnect between the threats our war-fighters and their families face and the tools they have to defend themselves," Senate Armed Services Chairman John McCain, R-Ariz., and House Armed Services Chairman Mac Thornberry, R-Texas, said in a joint statement.

The two are negotiating a final version of the legislation that's expected to be considered by the end of the month.

Meanwhile, two Tennessee House members, Republican Scott DesJarlais and Democrat Steve Cohen, introduced legislation Monday that would require the Pentagon to allow service members with firearms training to carry their weapons to work.

Governors in Texas, Oklahoma, Arkansas, Louisiana, Indiana and Florida already have authorized National Guard troops to carry arms at facilities in their states for self-defense, using their authority under Title 32 of the U.S. Code, along with beefed-up police protection for those sites.

"I think it is imperative that we ensure that those who have stepped forward to defend our state and our nation have the ability to defend themselves," Indiana Gov. Mike Pence said Sunday at a news conference. "And the action that I am taking as governor will see to it that our Indiana National Guard has the ability to do just that."

Northern Command spokeswoman Army Maj. Beth Smith hinted on Monday that at least some local commanders may follow that example when asked if recruiters and reservists — who are under the federal government's control — will be allowed to carry arms.

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