The American Civil Liberties Union is asking a judge to order Michigan to recognize more than 300 same-sex marriages performed in March.
A lawsuit was filed in April, but the case is moving slowly.
The state still has until June 5 to respond. So the ACLU's Michigan branch took a different step Thursday by seeking a preliminary injunction.
It means federal Judge Mark Goldsmith could make a decision before the entire case is finished.
Governor Rick Snyder says the state won't recognize more than 300 same-sex marriages that were performed a day after a judge struck down Michigan's gay-marriage ban. There have been no additional marriages while the case is being appealed.
Snyder says state recognition should wait until the appeals end. The federal government is recognizing the marriages.