The Senator, who is thought to want to stand for the Republican presidential nomination in 2016, made the comments during an interview on Fox News with Bret Baier on Friday.
The interview covered a range of topics for the potential nominee, including his views on the economy, defence and security.
But Baier also questioned him on whether critics were right that he has been moderating his values on social issues to fit for a presidential run.
The self-described “libertarian conservative” insisted this was not the case, explaining that while he supports marriage, it “offends” him and others that the institution could be extended to gay and lesbian Americans, citing that “competing contracts” should have been issued instead.
“I’m for traditional marriage. I think marriage is between a man and a woman,” said Paul.