Ted Cruz: I 'salute' Donald Trump for discussing immigration

Republican presidential candidate Ted Cruz backed the general sentiments of Donald Trump's broadside against illegal Mexican immigrants, though he said he would use different words.

Asked whether he agreed with Trump's comments that Mexican immigrants were coming to the U.S. and raping women, he said, "To be clear, what I salute him for is focusing on the problems of illegal immigration."

He blamed the controversy in part on the media.

"Sometimes it seems there's no sport that the media enjoys more than Republican-on-Republican violence," Cruz said during an interview at the Delivering Alpha conference presented by CNBC and Institutional Investor.

He said he would refuse to engage in attacks against his opponents, though he did single out Jeb Bush, Marco Rubio and Scott Walker for endorsing amnesty for illegal immigrants.

Read MoreSen. Ted Cruz blames the media for distorting his image

"Policy disagreements are meant to be the bread and butter of politics," Cruz, a Texas senator, said. "I don't think it's appropriate to impugn the integrity of other candidates, and I don't intend to do so."

Indeed, he spent most of the interview not distancing himself from his Republican competitors but rather criticizing the likely Demcoratic nominee, Hillary Clinton, as well as President Barack Obama.

He joked that "There are a lot of young people with faded posters of hope and change sleeping in their parents' garage."

Senator Ted Cruz speaking at Delivering Alpha 2015 in New York.
Adam Jeffery | CNBC
Senator Ted Cruz speaking at Delivering Alpha 2015 in New York.

Specifically addressing the crowd of investing professionals in the audience, Cruz championed the free market while also saying the Obama administration has been the best friend to big business. In fact, he said he would seek to "deliver alpha" in Washington government.

"A lot of the folks in here have done very well, but they don't necessarily come from money," he said. "A lot of the people in here started in the mailroom."

"You want to sum up this race in one simple meme? It's one we tweeted out," Cruz added. "Reaganomics, you start a business in your parent's garage; Obamanomics you move into your parents garage."

Onerous regulation has been a major problem for business, he said.

The current government "is a thug and an enforcer—how many Wall Street firms has the Obama administration has come after?" he said. "I think the Democrats are the party of the rich, of big government cronyism."

—CNBC.com's Marguerite Ward contributed to this report.