Towards the end of the exchange, Wallace brought up a list of "dirty tricks" allegations against the Cruz campaign.
"Do you take personal responsibility for this series of incidents and what does it say about the culture of the campaign you're running?" Wallace asked on "Fox News Sunday."
Among thee the things Wallace cited was Cruz's campaign incorrectly suggesting that Ben Carson was about to drop out of the race during the Iowa caucuses, and Cruz's spokesman sharing a news article that incorrectly quoted Marco Rubio commenting about the Bible.
But Cruz dismissed the premise of the question.
"Chris, every accusation you raised there is incorrect. I appreciate you reading the Donald Trump attack file on that," the Texas senator told Wallace.
Wallace then interjected as Cruz repeatedly said: "Chris, please don't interrupt me." The two continued to talk over one another.
"Oh come on," Wallace said. "You personally apologized to Ben Carson on a debate stage. You fired your communications director. Don't say that this is an oppo file on our part," he added.
"Chris, please don't interrupt me," Cruz said for the fourth time.
"Well, I mean, please don't accuse me of something I didn't do," Wallace replied.
"Go ahead. Go ahead Chris. Let me know when I'm allowed to answer," Cruz said.
"Well, don't accuse me of something I didn't do," Wallace reiterated.
Cruz then said he had been running a campaign of "the highest level of integrity." He also told Wallace it was "striking" that, earlier in the show, the Fox host didn't grill Trump for repeating a false quote from Sen. Tom Coburn, or for a reported robocall from a white supremacist group that backed Trump.
"First of all, I don't think anybody is going to think I did an easy interview with Donald Trump," Wallace shot back. "I asked him about plenty of things. If you want to ask him those questions, guess what, you'll get the opportunity at the Fox debate next Thursday."
Watch part of their interview below:
Sen. Ted Cruz (R-TX), Presidential candidate, denies what people are calling "dirty tricks" by his campaign. What are your thoughts on the 2016 race for President? For the full interview, tune into the Fox News Channel at 2pm & 6pm EST.
Posted by Fox News Sunday on Sunday, 28 February 2016