Cruz goes further with his bill, which would prohibit refugees from Iraq, Libya, Somalia, Syria and Yemen from entering the United States. The State Department has said those countries are controlled in part by a foreign terrorist organization.
"After watching the horrific scenes play out in Paris, we have to take basic steps to protect ourselves from the growing threat of radical Islamic terrorism. This legislation will do just that," Cruz said in a statement.
Cruz has said there is "not a meaningful risk" that Christians are committing terrorism, but has not said how he would determine the religion of refugees. The bill mandates that the Department of Homeland Security "may not admit any refugee based solely on the assertions of the refugee," according to Cruz's office.
"DHS cannot simply take the refugee’s word for it," a statement from Cruz's office reads. The bill requires coordination with a number of federal agencies, including the director of the FBI.
The bill does not mention religion, but says that the person should be admitted if he or she "clearly proves, beyond doubt" that he or she "satisfies the requirements for admission as a refugee; and is a member of a group that has been designated by the Secretary of State or by an Act of Congress as a victim of genocide."
President Obama has blasted Cruz and other Republican presidential candidates for wanting to keep Syrian refugees from entering the United States, calling it a "potent recruiting tool" for the Islamic State.
The Texas Republican often mentions how his father fled Cuba for the United States as a young man. Cruz was asked on CNN on Monday how he could bar refugees from the United States given his father's story.
"If my father were part of a theocratic and political movement like radical Islam that promotes murdering anyone who doesn't share your extreme faith or forcibly converting them, it would make perfect sense not to let someone in who embraces political philosophy and theology that says murder the infidels," Cruz said.