Charleston, SC (CNN) Ted Cruz may believe that Christian refugees from Syria pose no risk to American security, but he is open to looking beyond religion and actually vetting those emigrants, he said in a new interview.

The rising presidential candidate is aligning himself with the most restrictionist voices in the debate over how to handle the refugee crisis, which is dominating the Republican race after a deadly attack in Paris left more than 100 dead. Cruz has applied a "religious test" to judge which refugees to admit, in the words of the White House, telling reporters across South Carolina this weekend that he would admit all persecuted Christians to the U.S. but no persecuted Muslims.

But in an interview with CNN's Dana Bash on Monday, Cruz conceded that he would support measures to sift through the Christian refugees should ISIS militants try to disguise their identities.

"There is no doubt we would need to vet anyone coming in, but there is no indication that we have Muslims pretending to be Christians in the coming refugee wave," Cruz said before an event at the College of Charleston, concluding his three-day swing across the Palmetto State. "If that develops to be a problem, then our first obligation should be protecting our national security."

Cruz, like other Republican hardliners, has argued that the risk of Islamic militants infiltrating the refugee population is too high for America to accept them with open arms. On the stump across South Carolina, Cruz argued that the percentage of refugees that are young men suggests that ISIS may look to take advantage of any relaxation of immigration laws.

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