Republican presidential candidate Rand Paul tried in a recent interview to square his libertarian ideology with his desire to appeal to conservative voters who do not approve of same-sex marriage.

During an interview that aired on Sunday, CNN's Dana Bash pointed out that Paul had told voters in New Hampshire that he would "fight for your right to be left alone."

"Why do you believe -- just as a core principle as a libertarian -- that people should be left alone, but not when it comes to their right to marry someone they love?" Bash wondered.

"I do believe people ought to be left alone," Paul insisted. "I don't care who you are, what you do at home or who your friends are, where you hang out, what kind of music you listen to. What you do in your home is your own business. That's always been who I am. I am a leave-me-alone kind of guy."

"But not when it comes to marriage," Bash noted.

"Well, no, the states will end up making the decisions on these things," Paul replied. "I think there's a religious connotation to this. I also believe people ought to be treated fairly under the law. I see why if the marriage contract conveys certain things, that if you want to marry another woman, you can do that and have a contract. But the thing is that the religious connotation of marriage that has been going on for thousands of years, I still want to preserve that."

"And you probably could have both," he continued. "You could have both the traditional marriage, which I believe in and then you could also have the neutrality of the law that allows people to have contracts with another."