Republican presidential hopeful Rand Paul, who has called legalization of same-sex marriage offensive and a sign of “moral crisis,” is keeping up his opposition to marriage equality while saying same-sex couples should enter into contracts to formalize their relationships.

Speaking to Dana Bash on CNN’s State of the Union Sunday, Paul said he believes in “the traditional religious connotation” of marriage, which is that it is reserved for male-female couples. “I also believe people ought to be treated fairly under the law,” said Paul, a U.S. senator from Kentucky.

“And you probably could have both,” he continued. “You could have both 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.”

He did not elaborate on what such a contract would be — legal marriage, civil union, or simply a private arrangement negotiated with a lawyer.

In a March interview on Fox News, Paul said using the term “marriage” for same-sex unions “offends myself and a lot of people” but called for some form of contract that would give same-sex couples “equivalency before the law.” Later in the month, he spoke at a prayer breakfast where he twice used the phrase “moral crisis” to describe life in the U.S., once applying it directly to marriage equality.

Paul declared his presidential candidacy last week. Watch his interview with Bash below, courtesy of Raw Story.