Republican presidential candidate Ted Cruz speaks to supporters at a rally at the Durango Hills Community Center in Las Vegas on Feb. 22, 2016. (Photo by Ricky Carioti/ The Washington Post)

This post has been updated

Sen. Ted Cruz (R-Tex.) significantly sharpened his stance on immigration Monday, stating that he would find and deport the more than 11 million undocumented immigrants living in the United States.

"Yes, we should deport them," Cruz said on Fox News. When asked by host Bill O'Reilly if he would "look for them," Cruz said yes.

"Of course you would. That's what ICE exists for," Cruz said, using an acronym for Immigration and Customs Enforcement. "We have law enforcement that looks for people who are violating the laws that apprehends them and deports them."

The statement is a marked shift for Cruz, who had long avoided the question of what he would do with the millions of people living in the country illegally. In December, Cruz said he opposes granting people here illegally legal status.

Just last month, Cruz said he opposes a special force to deport undocumented immigrants. The way to catch people, he said, is through things like the e-verify system and traditional law enforcement.

"Are they gonna knock on every door in America? No," Cruz told CNN's Jake Tapper. "I don't intend to send jackboots to knock on you door and every door in America. That's now how we enforce the law for any crime."

O'Reilly Monday gave Cruz a hypothetical example: if a man from Cork, Ireland, overstays his visa, settles into life on Long Island and has a few children, would Cruz send federal authorities to his house to find and deport him?

"You'd better believe it," Cruz said. "Right now we can't actually do that becuase we don't have a biometric exit entry system, so we don't know" when someone leaves.

Republican front-runner Donald Trump has promised he would create a deportation force to find and expel undocumented immigrants.

Cruz's comments come after a disappointing third-place finish in South Carolina Republican primary on Saturday. The senator has continually hit Trump on immigration, stating that the businessman once supported granting citizenship to undocumented immigrants, a position known as "amnesty."

Cruz has long assailed his other rival, Sen. Marco Rubio (R-Fla.), for co-sponsoring a bill that would have granted citizenship to undocumented immigrants.