Sen. Rand Paul (R-Ky.) on Wednesday appeared to suggest a link between the Supreme Court's rulings on gay marriage and marriage between a human and a non-human, but later walked back that suggestion and said it was a joke.

"It is difficult, because if we have no laws on this, people will take it to one extension further  -- does it have to be humans?" Paul said Wednesday in an interview with Glenn Beck, after Beck suggested some unintended consequences of the rulings, including polygamy.

Paul's office said that the senator was making a joke.

"Sarcasm sometimes doesn’t translate adequately from radio conversation," spokeswoman Moira Bagley said. "Sen. Paul did not suggest that striking down DOMA could lead to unusual marriage arrangements. What he was discussing was that having the state recognize marriage without definition could lead to marriages with no basis in reality."

Later in Wednesday, on Fox News, Paul took a different tack, saying marriage as defined by each state "will probably be within certain parameters."

"Like I said, I don't think it will be with multiple humans, and I think it will be human and human," he said. "And so I didn't mean that to mean anything other than that I think the government will still probably be involved in defining marriage to a certain aspect. I don't think we're going on towards polygamy or things beyond that."

In another interview, with ABC News, Paul praised the Supreme Court's decision for allowing states to determine whether they will allow gay marriage.

Updated at 11:19 a.m.