Former Florida governor Jeb Bush called such a registry “abhorrent”, Florida senator Marco Rubio said the idea was “unnecessary” and not something Americans would support and Texas senator Ted Cruz, who has largely avoided criticising Mr Trump throughout the 2016 campaign, said he was “not a fan of government registries of American citizens”.
The first reference to a database came in a Trump interview with Yahoo News published on Thursday. When asked about requiring Muslims to register in a database or carry a form of special identification noting their religion, the billionaire property tycoon said: “We’re going to have to look at a lot of things very closely.”
Mr Trump was pressed on the idea of a registry by an NBC News reporter that evening. Asked if there should be a database system for tracking Muslims in the United States, he said: “There should be a lot of systems, beyond databases.”
The reporter asked if that was something Mr Trump would put in place as president. Mr Trump replied: “I would certainly implement that. Absolutely.”
He also told the reporter that Muslims would “have to be” registered.
But in a Fox News Channel interview, Mr Trump tried to clarify his position. “I want a watch list for the Syrian refugees that (President Barack) Obama’s going to let in if we don’t stop him as Republicans,” he said.
He also said that he had trouble hearing the NBC reporter’s questions.
He addressed the issue during a rally in Alabama later, telling the crowd that reports on his previous statements were inaccurate. But he also voiced support for additional surveillance, both of arriving refugees and certain mosques.
“So here’s the story just to set it clear: I want surveillance of these people. I want surveillance if we have to and I don’t care,” he said. “I want surveillance of certain mosques, OK.”
The terror attacks in Paris that killed 130 people and wounded hundreds more have raised fears in the US and prompted calls for new restrictions on refugees fleeing war-torn Syria.
The House of Representatives passed legislation in the past week essentially barring Syrian and Iraqi refugees from the United States. It is unclear whether the Senate could get enough votes to override a threatened veto by Mr Obama.
Civil liberties experts said a database for Muslims would be unconstitutional on several counts. The libertarian Cato Institute’s Ilya Shapiro said the idea violates basic privacy and liberty rights.
Marci Hamilton, a Yeshiva University legal expert on religious liberty, said requiring Muslims to register appears to be a clear violation of the US Constitution’s protection of religious freedom.
Democratic presidential front-runner Hillary Clinton told a Tennessee rally: “Mr Trump has attacked Mexican immigrants, he’s attacked women and now he’s attacking Muslim Americans. At some point you have to ask yourself, is that the kind of country we are?”
Ben Carson, the retired neurosurgeon who has challenged Mr Trump’s lead in the Republican race, said America should have a database on “every foreigner who comes into this country”, but he rejected the idea of tracking US citizens based on their religion. He said he would support government monitoring of “a mosque or any church or any organisation or any school or any press corps where there was a lot radicalisation and things that were anti-American”.