Wisconsin Governor Scott Walker on Sunday said that he would support a constitutional amendment excluding gay couples from marriage if the Supreme Court strikes down state bans on gay marriage.

Walker, a potential Republican presidential candidate, made his remarks during an appearance on ABC News' This Week.

“I personally believe that marriage is between one man and one woman,” Walker said. “If the court decides that, the only next approach is for those who are supporters of marriage being defined as between one man and one woman is ultimately to consider pursuing a constitutional amendment.”

“I believe that the decision defining marriage should be left up to the states,” he added.

The high court will hand down a decision this month in a case challenging bans in Michigan, Ohio, Tennessee and Kentucky. The ruling could strike down the nation's remaining 13 bans.

Gay and lesbian couples began exchanging vows in Wisconsin late last year after the Supreme Court refused to hear an appeal in a lower court's ruling invaliding the state's ban. Walker said in April that he's attended a same-sex wedding reception.