Republican presidential candidate Ted Cruz said Tuesday that fellow candidate Chris Christie's "oppo research guys" got their facts wrong when the New Jersey governor attacked Cruz during a Fox News appearance.

Christie, addressing comments Cruz made about not believing in "Republican-on Republican violence," said on Fox News Monday that he didn't "need to be lectured by Ted Cruz." Cruz made those comments when asked to comment on Donald Trump's controversial remarks on Mexican immigrants.

"I find it ironic that Ted Cruz is giving lectures on Republican-on-Republican violence," the New Jersey governor said on Fox News Monday. "The guy who put together a group that was sponsoring primary ads against Sen. Lamar Alexander is giving us – the rest of us lectures on Republican on Republican violence. With all due respect, I don't need to be lectured by Ted Cruz."

Cruz hit back at Christie Tuesday, saying his comments were factually wrong and adding that he "disagreed" with Christie's choice to attack other Republicans.

"Well listen, I like Chris Christie, I have repeatedly praised Chris Christie -- indeed, I've repeatedly and vocally defended Chris Christie from what I think are unfair and ridiculous attacks and charges on the whole Bridgegate thing, which I've said is water under the bridge," Cruz said on the Mike Gallagher Radio.

"You know, he can choose to say what he wants to say, you know -- I do appreciate his kind efforts to highlight that I have consistently worked hard to elect conservatives to Congress," said Cruz. "It is interesting his oppo research guys got the facts wrong, because I did not actually get involved in Lamar Alexander's race."

Christie was citing Cruz's connections to the Senate Conservatives Fund (SCF), a group known for supporting primary challenges to Republican incumbent senator when he made the comments. SCF never actually endorsed Alexander's primary opponent and Cruz did not endorse in the race.

"But, you know, at the end of the day, if he or anyone else wants to attack their opponents, they can choose to do that," concluded Cruz. "I disagree with that choice. I am going to sing Chris Christie's praises, I'm gonna sing Donald Trump's praises, and I'm going to focus on the issues that matter, which is turning this country around, which is fighting to restore the Constitution, to defend our liberties, to bring back jobs, and growth, and opportunity, and to restore America's leadership in the world. That's what the American people want, not a bunch of self-centered politicians bickering like children in Washington."