Republican presidential candidate Ted CruzRafael (Ted) Edward CruzWhatever you think the Alabama special election means, you’re probably wrong This week: Congress gets ball rolling on tax reform Week ahead: Senators work toward deal to fix ObamaCare markets MORE said on Sunday that he has no plans to "insult" GOP front-runner Donald TrumpDonald John TrumpIvanka Trump pens op-ed on kindergartners learning tech Bharara, Yates tamp down expectations Mueller will bring criminal charges Overnight Cybersecurity: Equifax security employee left after breach | Lawmakers float bill to reform warrantless surveillance | Intel leaders keeping collusion probe open MORE.

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"I'm not going to engage in personal attacks," Cruz said on CNN's "State of the Union." "No matter what he says, I like Donald."

"I do think policy differences are fair game," he added.

Cruz said that only a month ago, Trump was "telling everyone how much he liked me." But now, since Cruz has gained in the polls, he wakes up every morning to a new insult surfacing against him, Cruz added. 

"I will give him credit that when he insults someone, its always memorable and colorful," Cruz said of Trump.

Cruz also said that he and Trump have very different views, but said the voters deserve more than just petty insults.

In the past week, Cruz has shifted his criticism to Marco Rubio. In an ad in Iowa, Cruz called the Florida senator the "Republican Obama."

In response, Rubio said in an interview Sunday that he opposes “virtually everything Barack Obama stands for.” Rubio called it "strange" that Cruz would target him in the last few days before the Iowa caucuses.