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) on Tuesday admitted he might have “misspoken” when he said he had lobbied 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.) for hearings on letting U.S. troops carry personal firearms on military bases.

McCain said Monday that he and his staff hadn't heard from Cruz on the topic.

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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," McCain told reporters on Monday. "Where did that come from? I have not a clue.

“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," McCain said.

Cruz said Tuesday he had pressed McCain's committee on the issue.

“Now, I will acknowledge, I may have misspoken in New Hampshire when I said I had been pressing John McCain. What I had been pressing is the Armed Services Committee, and John McCain is the new chairman of it,” Cruz said during an interview on Fox News’s “America’s Newsroom.”

The 2016 presidential hopeful and Armed Services Committee member said he had raised the issue at panel hearings and sent a letter to former Chairman Carl Levin Carl Milton LevinMichigan to pay 0M to victims of Flint water crisis Unintended consequences of killing the filibuster Inspector general independence must be a bipartisan priority in 2020 MORE (D-Mich.) on the topic. He added, “but I had not communicated that 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, listen to the military’s arguments.”

A Cruz spokeswoman said the senator’s office is now drafting a similar letter to McCain.

Cruz and other lawmakers argue that, if soldiers are able to carry private firearms on military installations, they might be able to prevent mass shootings, such as the two that have occurred at Fort Hood.

“The military brass opposes this. We ought to hear their arguments, but I’m a big defender of defending the Second Amendment rights of everyone, including our soldiers,” Cruz said.

Their differences aside, Cruz said he likes McCain and said the veteran lawmaker "can always be counted on for a good quote."