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Democratic National Committee Chairwoman Debbie Wasserman Schultz is slamming Donald Trump for his "shameful" refusal to rule out a national database that keeps tabs on Muslims in the U.S.

Trump told Yahoo News, in an interview published Thursday, he would "look at a lot of things very closely" as president in regards to the country's Muslim population. Asked whether he would support monitoring Muslim-Americans by requiring their registration in a national database, the leading Republican hopeful, who's fourth in the Washington Examiner's presidential power rankings, declined to get specific.

"We're going to have to do things that we never did before. And some people are going to be upset about it, but I think that now everybody is feeling that security is going to rule," he said.

"Donald Trump's openness to special identifications and a database for Muslim-Americans is beyond shameful, embodies the exclusionary culture of today's Republican Party and is a dangerous mindset our Greatest Generation fought and died to defeat seven decades ago," Wasserman Schultz said in a statement Thursday afternoon.

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