Following some mocking comments made by fellow Sen. John McCain, Sen. Ted Cruz has backtracked on comments he made this weekend in New Hampshire claiming that he has been "pressing" the Arizona lawmaker to hold hearings on whether U.S. service members should be allowed to carry concealed weapons on military bases. Cruz believes that it should be allowed.

"Now I will acknowledge, I may have misspoken in New Hampshire when I said that I had been pressing John McCain, and what I had been pressing was the Armed Services Committee," Cruz said in an interview Tuesday on Fox News. "John McCain is the new chairman of it, so I sent a letter to the previous chairman."

Later on Tuesday, Rick Tyler of the Cruz presidential campaign said that the reports about what transpired were erroneous.

"Senator Cruz didn’t 'backtrack' on any comments he made and he did not misspeak," Tyler said to Fox News Latino. "After listening to a recording of Cruz’s remarks [at an appearance], it is clear that Senator McCain was reacting to something that Cruz did not say."

"One of the things I've publicly called for on the Armed Services committee is for us to have hearings on why the military has a policy of not allowing soldiers to carry their firearms onto bases," Cruz said in response to a question posed at the Londonderry Fish and Game Club in New Hampshire. "I want to give an opportunity for military leadership to lay out their views as well, because they have opposed changing that policy, and I think the proper way forward is to have hearings."

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"It's one of the things I'm pressing," Cruz said in his remarks, provided via a transcript to Fox News Latino by his campaign. "I hope the new chairman, John McCain, will agree to have those hearings because I think it’s very important to have a public discussion about why we’re denying our soldiers the ability to have their Second Amendment rights.”

Cruz's remarks as described in various media outlets come a day after McCain made some quips at the Texas lawmaker's expense.

"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 said, according to The Hill. "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," he added. "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 attempted to brush aside McCain's jests, claiming that the senior senator's response was "voluble" and that he "can always be counted on for a good quote." He added that he had raised the issue of military members being permitted to carry personal firearms on bases repeatedly in open hearings at which he believes McCain was present.

"I had not communicated [these policies] to John directly, although I had at a hearing and will continue to raise it with John McCain because the committee ought to look at and listen to the military's arguments," Cruz said.

"I'm a big believer in defending Second Amendment rights of everyone including our soldiers," he added.

For his part, McCain added on Twitter following Cruz's admission that, "Ted Cruz is a friend and valued member of the Senate Armed Services Committee."

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