Donald Trump is trying to back away from his support for a government database to track Muslims in the United States, an idea that drew sharp rebukes from his Republican presidential rivals and disbelief from legal experts.
Former Florida Governor Jeb Bush called the prospect of a registry "abhorrent".
Florida Senator Marco Rubio said the idea was "unnecessary" and not something Americans would support.
Texas Senator Ted Cruz, who has largely avoided criticising Trump throughout the 2016 campaign, said, "I'm 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, Trump said, "We're going to have to look at a lot of things very closely."
Trump was pressed on the idea of a registry by an NBC News reporter on Thursday evening. Asked if there should be a database system for tracking Muslims in the United States, Trump said, "There should be a lot of systems, beyond databases."
The reporter asked if that was something Trump would put in place as president. Trump replied: "I would certainly implement that. Absolutely."
Trump also told the reporter that Muslims would "have to be" registered.
In an interview on Fox News Channel on Friday evening, 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 addressed the issue during a rally in Alabama on Saturday, telling a 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," said Trump. "I want surveillance of certain mosques, OK."
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.