Cruz, speaking during his book tour in Marietta, Ga., said he likes Trump, who Cruz said is "bold" and "brash." Cruz said he's not going to attack Trump.
"I salute Donald Trump for focusing on the need to address illegal immigration," Cruz said, reiterating that he believes that "amnesty is wrong."
Cruz said Trump has a "colorful way of speaking -- it's not the way I speak. But I'm not going to engage in the media's game of throwing rocks and attacking other Republicans. I'm just not gonna do it."
Cruz previously said that Trump was "terrific" and shouldn't apologize because he "speaks the truth."
A number of GOP candidates condemned Trump's comments.
"They're bringing drugs," Trump said in his presidential announcement speech. "They're bringing crime. They're rapists."
Trump also said he wants to build a "great wall on our southern border" to keep illegal immigrants from Mexico out of the United States.