WASHINGTON — (CNN) Lawmakers in Washington are moving quickly on legislation to allow trained members of the military to carry guns on bases and recruiting centers, but Pentagon officials and military commanders are exploring whether the possible legal change could raise additional security concerns.

Rep. Duncan Hunter of California and Sen. Steve Daines of Montana, both Republicans, introduced a bill Tuesday that allows the military to authorize those who work at recruiting centers to be armed and permits security enhancements at those facilities.

On Monday, Democrats and Republicans from Tennessee introduced legislation in the House of Representatives that would lift a directive issued by the Pentagon over 20 years ago that barred most servicemen from carrying firearms at military installations.

The efforts come in the wake of the shooting at a military recruiting office in Chattanooga Thursday that left five dead.

“Far too often we have witnessed horrific acts of violence carried out against members of our armed forces right here in the United States,” GOP Rep. Scott DesJarlais of Tennessee said in a statement announcing the bill.

Democratic Rep. Steve Cohen added, “Those who volunteer to protect Americans abroad should not be prevented from protecting themselves when they return home.”

The House bill specifies that those able to carry guns would be required to have weapons training. It also mandates that firearms carried at posts or recruiting centers be issued by the military, ruling out anyone using personal guns.

Separately, Virginia Republican Rep. Scott Rigell, whose district includes one of the highest concentrations of those serving in the military, is collecting signatures on a letter to Defense Secretary Ashton Carter urging him to immediately change the current policy so that commanders can permit approved weapons on installations.

Carter has already asked the Pentagon and military commanders to make recommendations on improving safety at reserve, recruiting and ROTC centers by the end of the week.

The military review, though, is considering the possibility that arming active duty and national guard troops could raise additional safety issues. Factors that would have to be taken into account include emptying guns of ammunition and storing them in a secure, approved armory area; approving rules of engagement; and the stance of civilian authorities in places where these troops are present off bases.

It’s also not clear how and if recruiters could remain armed if they were to visit high schools or shopping malls or hold other public events in venues where carrying a weapon may not be allowed. Shopping mall owners that lease to the military recruiting centers and even universities that host ROTC units would have to approve any plans concerning the arming of individuals at their sites.

Under current law, active duty military troops are not permitted to engage in what is considered law enforcement activity, such as carrying arms and potentially firing their weapons in civilian areas.

Leaders of the Senate and House Armed Services Committees who are negotiating the annual defense authorization bill said that they were already looking at including a provision that would give military leaders at bases around the country the discretion to allow servicemen and women to carry guns.

“Together, we will direct the Pentagon to end the disconnect between the threats our warfighters and their families face and the tools they have to defend themselves,” Sen. John McCain and Rep. Mac Thornberry, both Republicans, said on Friday.

Asked about the bill proposed by the Tennessee delegation Tuesday, House Majority Leader Kevin McCarthy suggested the issue could be addressed as part of the final defense bill, which is expected to be on the House floor as early as next week. McCarthy also said he expected hearings on the issue.

In the wake of the attack in Chattanooga last week, several Republicans running for president — including Donald Trump, Jeb Bush and Chris Christie — also called for a review of current laws.

Kentucky Sen. Rand Paul, who is also seeking the Republican presidential nomination, also told a group of reporters who visited his campaign office that he was drafting legislation that is similar to the bill introduced by House members, according to a report in the Washington Post.

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