Appealing to New Hampshire’s powerful gun culture, Sen. Ted Cruz said Sunday that he’s “pressing” Senate Armed Services Committee Chairman John McCain to hold hearings on whether soldiers should be allowed to carry their own concealed firearms onto military bases.

“I am very concerned about that policy,” the Texas senator told 120 gun owners at a hunting club here, before taking a trip to a firing range for some target practice. “I think it’s very important to have a public discussion about why we’re denying our soldiers the ability to exercise their Second Amendment rights.”

Defense Department leaders oppose relaxing the ban, which was enacted under George H.W. Bush.