Republican presidential candidate Ted CruzRafael (Ted) Edward CruzConservatives express concern over House GOP immigration bill GOP senators introduce bill to prevent family separations at border Senate GOP tries to defuse Trump border crisis MORE said on Sunday that he has no plans to "insult" GOP front-runner Donald TrumpDonald John TrumpConservatives express concern over House GOP immigration bill Poll: McSally holds 14-point lead in Arizona GOP Senate primary Trump defends Nielsen amid criticism over family separations 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.