Ben Carson says creating a registry to track Muslims, an idea floated by GOP presidential rival Donald Trump, sets a "pretty dangerous precedent."

"I think we should have a database on everybody who comes into this country," Carson told reporters on Friday in New Hampshire, where he filed to be on the primary ballot.

Pressed by a reporter on whether he would denounce Trump's call for a database focused specifically on registering Muslim Americans, Carson rejected the idea of filtering people based on their religion.

"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. 

"So if we're just going to pick out a particular group of people based on their religion, based on their race, based on some other thing — that's setting a pretty dangerous precedent, I believe," he added.

Trump was roundly criticized by Democrats and some GOP rivals, including former Gov. Jeb Bush (Fla.), for suggesting the U.S. should create a database to track Muslims living in the country.

Trump also said this week that he supported closing some mosques to defeat Islamic militants and prevent another terrorist attack after the violence in Paris last week. He has also pushed back strongly against admitting refugees from Syria into the U.S.

The GOP front-runner appeared to double down on his calls in recent days, but on Friday distanced himself from the comments on Twitter, saying, "I didn't suggest a database-a reporter did." 

Asked Friday if he favored more monitoring for mosques in the U.S., Carson said, "I favor doing anything that we have to do to protect the American people."

"If, in fact, there are mosques where there is a lot of activity going on that's radicalizing people, they must be treated differently," he said, later clarifying he would apply the same standard to institutions of any faith, including Christian ones.