Wednesday's lawsuit was filed by the same law firm that filed a February suit that led a federal judge to order Ohio to recognize out-of-state same sex marriages.
In his April 14 order, Judge Timothy Black said Ohio's refusal to recognize gay marriage is a violation of constitutional rights and "unenforceable in all circumstances."
"The record before this court ... is staggeringly devoid of any legitimate justification for the state's ongoing arbitrary discrimination on the basis of sexual orientation," Black wrote.
His order stopped short of forcing Ohio to allow gay couples to wed in the state.
Although most of the ruling is on hold pending DeWine's forthcoming appeal in the 6th U.S. Circuit Court of Appeals, Black did order Ohio to immediately recognize the marriages of the four couples who filed the February sued by listing both spouses in each relationship on their children's birth certificates.
In a similarly narrow order in December, Black ordered Ohio to recognize gay marriage on death certificates.
Separately from the flurry of court action, FreedomOhio is seeking to put gay marriage back on the Ohio ballot as early as November, asking voters to require that all legally valid marriages be treated equally under the law, while keeping clergy from being forced to perform same-sex marriages.
Phil Burress, who led the 2004 effort to ban same-sex marriage, has said his group is prepared to fight any ballot initiative to repeal the ban.
He said he's confident that appeals courts will overturn Black's order and other recent rulings nationwide in favor of gay marriage.
Gay marriage is legal in 17 states and Washington, D.C. Federal judges recently have struck down gay marriage bans in Michigan, Utah, Texas, Oklahoma and Virginia, though stays have been issued pending appeals.
Similar to Ohio's ruling, judges in Kentucky and Tennessee have ordered state officials to recognize out-of-state gay marriages. Both those orders also have been put on hold.