"I think we should have a database on everyone who comes into this country," the retired neurosurgeon told reporters from the New Hampshire statehouse Friday, adding later, "Hopefully, we already have a database on every citizen who is already here. If not, we are doing a very poor job."

Trump's comments came Thursday after NBC News asked the real estate mogul if there should be a database to keep track of Muslims in the country.

"There should be a lot of systems, beyond databases. We should have a lot of systems," Trump said.

Indeed, the U.S. does have pre-existing large databases -- including U.S. Census data and the Social Security Administration, though it was unclear from Carson's remarks if those were the databases he was referring to.

When asked about a database focused on religion, Carson added that he didn't think it was a "good idea" to treat any group of people differently.