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"I think we should have a database on everyone who comes into this country," Carson said

Carson added that he didn't think it was a "good idea" to treat any group of people differently

CNN  — 

While Donald Trump is facing heat for apparently supporting the idea of a database of Muslims in the U.S., GOP primary opponent Ben Carson also wants a database – of everyone in the country.

“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.

RELATED: Trump would ‘certainly implement’ national database for U.S. Muslims

“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.

“One of the hallmarks of America is that we treat everyone the same,” Carson said, adding later, “I favor doing whatever we need to do to protect the American people.”

Carson was in the state filing his primary paperwork – as all presidential hopefuls must do and many have already – to get on the New Hampshire ballot.

CNN’s Jeremy Diamond contributed to this report.