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NEWTON, Iowa — Donald J. Trump, who earlier in the week said he was open to requiring Muslims in the United States to register in a database, said on Thursday night that he “would certainly implement that — absolutely.”

Mr. Trump was asked about the issue by an NBC News reporter and pressed on whether all Muslims in the country would be forced to register. “They have to be,” he said. “They have to be.’’

When asked how a system of registering Muslims would be carried out — whether, for instance, mosques would be where people could register — Mr. Trump said: “Different places. You sign up at different places. But it’s all about management. Our country has no management.’’

Asked later, as he signed autographs, how such a database would be different from Jews having to register in Nazi Germany, Mr. Trump repeatedly said, “You tell me,” until he stopped responding to the question.

Both Mr. Trump and Ben Carson, the top two Republican presidential candidates in most polls, have made sharply provocative remarks about Muslim refugees from Syria and Iraq, and have been criticized by Muslim groups in the United States.

On Thursday, Mr. Carson seemed to equate refugees’ seeking entrance to the United States to “a rabid dog running around your neighborhood.’’ Both Mr. Carson’s and Mr. Trump’s remarks came the day the House voted to severely restrict the flow of Syrian and Iraqi refugees into the United States, amid security concerns after the terrorist assaults in Paris.

Donald Trump’s Call for Muslim Registry Denounced by Democrats Donald J. Trump’s remarks took hours to penetrate over social media, but by Friday morning, Democrats were calling him out. Jeb Bush was one of the first Republican presidential candidates to respond, calling Mr. Trump’s words “just wrong.”

Donald Trump Steps Back From Calling for Muslim Registry Mr. Trump said the idea that Muslims in America should register with the federal government had come from a reporter.

Donald Trump Sets Off a Furor With Call to Register Muslims in the U.S. Mr. Trump drew back from his call for a mandatory registry of Muslims in the United States, capping a week where candidates discussed their approaches to terrorism.

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