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Sun Prairie -- Speaking to reporters after a campaign event at a farm here, GOP Gov. Scott Walker said the state was abandoning its fight to keep its same-sex marriage ban.

Walker made his remarks after the U.S. Supreme Court Monday rejected the state's appeal of a lower court ruling striking down Wisconsin's ban.

The governor, a named defendant in the lawsuit by eight same-sex couples, said he had voted for Wisconsin’s ban in 2006 and hadn’t changed his support for it, but he said he was accepting the Supreme Court’s decision.

Asked if the U.S. Constitution should be amended to ban same-sex marriage, Walker downplayed the notion, saying, “I think it’s resolved.”

“For us, it’s over in Wisconsin,” Walker said of the fight over gay marriage. “Others will have to talk about the federal level.”

Walker’s opponent, Democrat Mary Burke, embraced the decision.

“Today’s ruling marks an important step forward for Wisconsin. No loving, committed couple should ever be denied the freedom to marry — and those who have stood in the way of this progress, including Gov. Walker, are squarely on the wrong side of history,” Burke said in a statement.