Washington (CNN) Rand Paul isn't endorsing same-sex marriage, but said Sunday that "people ought to be treated fairly under the law."

The Kentucky Republican senator who launched his 2016 presidential campaign this week talked about the semantics of marriage equality in an interview with CNN's Dana Bash on "State of the Union."

He said the decision on whether to allow same-sex marriage should be left to the states, and that he believes in "the traditional religious connotation" to marriage -- which religious conservatives believe should be reserved for one man and one woman.

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"I also believe people ought to be treated fairly under the law," he said

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