Texas Sen. Ted Cruz further distanced himself from Donald Trump's call for a "complete shutdown" of Muslims entering the United States, but did say the country should "focus very directly on the threat, which is radical Islamic terrorism," and said that should include closer monitoring of those who enter the country.

"Well, I disagree with Donald on that. He is welcome to discuss his policy ideas. That is not my view of how we should approach it," the Republican presidential candidate told NPR's Steve Inskeep in an interview that aired Wednesday on "Morning Edition."

The interview was conducted Tuesday, the day after Trump's controversial comments on banning Muslims.

Cruz pointed out that there are "millions of peaceful Muslims" both in the U.S. and globally, and closer monitoring of those who enter the country, especially as it pertains to refugees, "is not about the Islamic faith."

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