A spokesman for Schimel did not immediately respond to a request for comment.

Thiesfeldt called for the registry to be repealed in June 2015, after the Supreme Court issued its ruling.

"The domestic partnership law is discriminatory. But it needs to be repealed, not expanded. It stands as a form of 'marriage-lite,' encouraging same-sex couples to avoid the commitment of marriage," Thiesfeldt said in a statement. "These clerks are now engaging in social engineering by lawlessly extending this 'marriage-lite' option to opposite-sex couples as well."

The state's domestic partnership registry was enacted by Democratic former Gov. Jim Doyle in 2009 as part of the state budget, three years after a ban on same-sex marriage was approved by voters.

While the state registry applies only to same-sex couples, Dane and Milwaukee counties have local ordinances that allow opposite-gender couples to register as domestic partners, as well.