Republican presidential candidate Donald Trump has drawn criticism from White House rivals for saying he would implement a database to keep track of Muslims in the United States and require them to register in response to the attacks in Paris.

Trump, speaking to an NBC News reporter after a campaign appearance in Iowa on Thursday night, was asked if there should be a database to monitor Muslims in the United States.

“I would certainly implement that, absolutely,” he said in on-camera comments. Asked how that differed from efforts last century to track Jews in Nazi Germany, he said: “You tell me.”

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On Friday, Trump deflected criticism of the remarks, saying in a tweet: “I didn’t suggest a database, a reporter did. We must defeat Islamic terrorism & have surveillance, including a watch list, to protect America.”

His comments came amid renewed security concerns following the Nov. 13 Islamic State attacks in Paris that killed at least 129 people, and a political fight over U.S. plans to take in 10,000 refugees from Syria.

Two Republican presidential rivals, former Florida Gov. Jeb Bush and Ohio Gov. John Kasich, were the most critical of the database comments. Bush called them “just wrong.”

“It’s manipulating people’s angst and their fears,” he said on CNBC. “That’s not strength. That’s weakness.”

Kasich, whose super PAC is launching a $2.5-million series of attacks against Trump, said the remarks proved the real estate mogul was not worthy of the White House.

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“The idea that someone would have to register with the federal government because of their religion strikes against all that we have believed in our nation’s history,” Kasich said in a statement.

Texas Sen. Ted Cruz, campaigning in Iowa, said he was glad Trump was running because he had generated a lot of excitement for the Republican race, but criticized his support for registries.

“On the question of should the federal government keep a registry of any religious group? The answer is of course not. The First Amendment protects religious liberties for every American,” Cruz said.

Retired neurosurgeon Ben Carson, who earlier compared Syrian refugees to “rabid dogs,” called singling out an individual religion to create a database “a pretty dangerous precedent.”

“I don’t think it’s a good idea to treat anybody differently, one of the hallmarks of America is that we treat everybody the same,” Carson said.

He said, however, it would be acceptable to shut down mosques where “a lot of activity going on that is radicalizing people.”

Other Republican candidates opted not to weigh in on the remarks from Trump, who earlier in the week called for shutting down American mosques frequented by radicals.

Trump, who leads the Republican presidential field in opinion polls, has called for deporting the estimated 11 million illegal immigrants in America. He said Muslims would be legally required to register for the database.

“There should be a lot of systems, beyond databases,” he said.

U.S. Democratic presidential candidate Hillary Clinton speaks during a campaign rally at Fisk University in Nashville, Tennessee, November 20, 2015. REUTERS/Harrison McClary

“This is shocking rhetoric. It should be denounced by all seeking to lead this country,” former Secretary of State Hillary Clinton, the Democratic front-runner, said on Twitter. Sen. Bernie Sanders of Vermont called Trump’s remarks “outrageous and bigoted.”

The Paris attacks have launched a growing debate on the 2016 campaign trail about the appropriate U.S. response.

Related: Paris Archbishop Offers Comfort

As the debate over terrorism has gained prominence, polls show Republicans turning to Trump, a billionaire with no previous government experience, to tackle the issue. A Reuters-Ipsos poll after the attack found 33 percent of Republicans surveyed think he is best suited to address terrorism, leading the field.

Trump supporters Betty and Terry Phelps, of Lisco, Nebraska, said the database made sense. Betty Phelps said it would not be much different from existing databases.

“We’re all kept track of, through driver’s license, social security number,” she said.

Ibrahim Hooper, spokesman for the Council on American-Islamic Relations, a Muslim rights group, said other Republican candidates should say whether they would close mosques, create a database of Muslims or require Muslims to carry a special ID card.

“This is way beyond the pale, this is basically a call to persecute a religious minority based on nothing other than their faith,” Hooper said.

This article originally appeared in Religion News Service and in Reuters.