Dr. Ben Carson, a prospective Republican presidential candidate, said Monday people should not be allowed to refuse vaccines on religious or philosophical grounds.

"Although I strongly believe in individual rights and the rights of parents to raise their children as they see fit, I also recognize that public health and public safety are extremely important in our society," Carson said in a statement to BuzzFeed News.

Carson said diseases of the past should not be allowed to return because of people avoiding vaccines on religious or philosophical grounds.

"Certain communicable diseases have been largely eradicated by immunization policies in this country and we should not allow those diseases to return by foregoing safe immunization programs, for philosophical, religious, or other reasons when we have the means to eradicate them," Carson said in the statement.

"Obviously there are exceptional situations to virtually everything and we must have a mechanism whereby those can be heard," he said.

BuzzFeed News asked Carson whether vaccinations for diseases like measles and rubella should be mandatory except in cases where a child's health does not allow it, and whether states should allow philosophical and religious exemptions.

Monday saw two other Republican presidential candidates weigh in on vaccinations.

Republican Gov. Chris Christie of New Jersey said while his children are vaccinated, the government must "balance" parents having "choice" in vaccinations.

Republican Sen. Rand Paul said Monday many vaccines should be voluntary, adding he has heard "many" cases of people getting mental disorders after taking vaccines.

"I have heard of many tragic cases of walking, talking normal children who wound up with profound mental disorders after vaccines," he told CNBC.