Cruz speaks at Tuesday's debate. (Robyn Beck/AFP/Getty Images)

Sen. Ted Cruz said Tuesday he opposes granting legal status to the 11 million undocumented immigrants in the United States, significantly hardening his stance on immigration.

Cruz has repeatedly sidestepped the question of what to do with undocumented immigrants currently living in the country, asserting that the U.S.-Mexico border must be secured before addressing the issue. A plan for what to do with undocumented people living in the country was conspicuously absent from an immigration proposal Cruz unveiled last month.

It is the farthest Cruz has gone on the issue, and the answer came during the Republican debate in an exchange with Sen. Marco Rubio (R-Fla)., with whom Cruz has repeatedly tangled over the issue of immigration.

Read: It’s on — Rubio and Cruz clash over immigration and the GOP’s future

“I have never supported legalization, and I do not intend to support legalization,” Cruz said.

Cruz's campaign chairman, Chad Sweet, told reporters after the debate that the candidate "unequivocally" rejects granting undocumented people legal status.

In an interview with CNN, Cruz said he would "enforce the law" and first deport criminals who are in the country illegally. Immigration law, he said, "provides that if someone is here illegally and is apprehended, that they should be sent back to their home country."

When asked about enforcement, Sweet said the campaign supports "attrition through enforcement," which some Hispanic groups who met with Cruz's campaign said they are concerned means self-deportation, or making life so difficult for undocumented people that they return to their home countries. Mitt Romney supported self-deportation as the Republican nominee in 2012.

A number of Cruz's positions on immigration have shifted in the past few years. Cruz, who bills himself as a "champion of legal immigration," once supported doubling the caps on green cards and increasing the number of the visas for high tech workers – known as H1-B visas – fivefold. Cruz now wants new limits on legal immigration and to temporarily halt the H1-B program, which has been rife with reports of abuse. He introduced a bill to reform it this month.

Read: Cruz takes the gloves off, attacking Rubio on immigration

Cruz has accused Rubio of being too soft on immigration because he co-sponsored a comprehensive Senate bill that would have created a path to citizenship for undocumented immigrants. Cruz refers to the legislation, which died in the House, as “amnesty," and the Texas Republican has long opposed allowing undocumented immigrants a way toward citizenship. On the debate stage Tuesday, Cruz tied Rubio's support for the bill to President Obama and Sen. Chuck Schumer (R-N.Y.)

Rubio claims that he and Cruz have very similar views on immigration, noting that Cruz pushed an amendment that would have allowed undocumented people to receive work permits. The amendment prevented them from obtaining citizenship. Cruz's campaign said the legislation was meant as a poison pill.

Cruz released his immigration plan in Orlando last month — on Rubio's home turf. Cruz said he would halt increases in immigration "so long as American unemployment remains unacceptably high," but didn't say what the threshold would be for allowing more people to enter the country."

Read: Ted Cruz unveils immigration plan — on Marco Rubio’s home turf

He skirted the question of what to do with the 11 million undocumented in the country, stating: "Consistently the approach of the Democrats and the media is to focus on the people who here illegally."

Cruz wants to triple the number of Border Patrol agents, build a wall on the U.S.-Mexico border and increase surveillance there. He also wants to end birthright citizenship — the process by which any baby born in the United States is granted citizenship, regardless of legal status of his or her parents.

"It's legal good, illegal bad," Cruz said about the immigration system in Orlando. "Why is that so complicated for anyone in Washington to understand?"

Sean Sullivan contributed reporting from Las Vegas