Senate Armed Services Committee Chairman John McCain John Sidney McCainMomentum growing among Republicans for Supreme Court vote before Election Day McConnell urges GOP senators to 'keep your powder dry' on Supreme Court vacancy McSally says current Senate should vote on Trump nominee MORE (R-Ariz.) is mocking Sen. Ted Cruz Rafael (Ted) Edward CruzVideo of Lindsey Graham arguing against nominating a Supreme Court justice in an election year goes viral Sunday shows preview: Justice Ginsburg dies, sparking partisan battle over vacancy before election Democrat on Graham video urging people to 'use my words against me': 'Done' MORE (R-Texas) for claiming he is “pressing” for hearings on allowing U.S. troops to carry private firearms on military installations.

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“You know, I was fascinated to hear that because I haven’t heard a thing about it from him. Nor has my staff heard from his staff. Where did that come from? I have not a clue,” McCain told reporters on Monday. “I’d be glad to discuss the issue and see if we need a hearing, but it came as a complete surprise to me that he had been pressing me.”

“Maybe it was through some medium that I’m not familiar with. Maybe bouncing it off the ozone layer, for all I know,” McCain joked. “There’s a lot of holes in the ozone layer, so maybe it wasn’t the ozone layer that he bounced it off of. Maybe it was through hand telegraph, maybe sign language. Who knows?”

Cruz's office issued a statement maintaining that the Texas Republican is not new to the issue.

"Senator Cruz has been discussing this issue for a long time and he looks forward to continuing to raise it in the Senate Armed Services Committee where he serves with Chairman McCain," according to the statement.

Cruz, a 2016 presidential candidate, made the most recent comments on Sunday while speaking at a campaign event in New Hampshire, according to Politico.

“I am very concerned about that policy,” Cruz said. “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.”

In recent years, GOP lawmakers, including fellow Texan, Rep. Louie Gohmert Louis (Louie) Buller GohmertRep. Dan Meuser tests positive for COVID-19 Watchdog calls for probe into Gohmert 'disregarding public health guidance' on COVID-19 Massie plans to donate plasma after testing positive for COVID-19 antibodies MORE, have pushed for the Defense Department to ease its ban on private firearms, citing mass shootings, such as the two that have occurred at Fort Hood in Texas. They contend such tragedies could have been avoided had soldiers been allowed to be armed.

Last week Gohmert urged the House Armed Services Committee to include a provision in its version of the annual defense policy bill to lift the ban.

A laughing McCain, who earlier on Monday chided Sen. Rand Paul (Ky.), another Republican presidential contender, over his understanding of foreign policy, said reporters should follow up with Cruz on how he sought hearings on the controversial issue.

“Ask him how he communicated with me because I’d be very interested. Who knows what I’m missing?” the Arizona Republican said.

— This story was updated on Tuesday at 9:16 a.m.