Equality Michigan, which advocates gay rights, sent an email to its members early Saturday with details of how to obtain marriage licenses. Clerks’ offices were also open and issuing marriage licenses in Oakland County, in suburban Detroit, and in Muskegon County, in western Michigan. Ms. Dievendorf said her organization was advising same-sex couples to consult with a lawyer before they marry and to make themselves aware of some of the legal complications stemming from the ban being reinstated while the appeal is heard.

Connie Greer, 46, and her partner, Diane VanDorn, 44, were among the couples who took advantage of the opportunity on Saturday in Ann Arbor. “It’s better to be in a legal purgatory than to have no legal standing whatsoever,” Ms. Greer said. “At least we’ve got our foot in the door.”

Before Friday’s ruling, same-sex marriages were legal in 17 states and the District of Columbia. And since June, when the Supreme Court struck down parts of the Defense of Marriage Act, which prohibited the federal government from recognizing same-sex marriages legalized by the states, all federal benefits to married couples have been extended to gays.

In 2004, Michigan voters approved an amendment to the State Constitution that made it unconstitutional for the state to recognize or perform same-sex marriages or civil unions. The measure, approved by 59 percent of the voters, said that “the union of one man and one woman in marriage shall be the only agreement recognized as a marriage or similar union for any purpose.”

Four years later, the Michigan Supreme Court ruled that the ban extended to the domestic partnership benefits for public employees, like health insurance. The case decided on Friday was brought by April DeBoer and Jayne Rowse, nurses who live together in a Detroit suburb and who each adopted children born with special needs and are raising them as one family. They originally sued in 2012 to overturn a state law that prevents them, as unmarried parties, from adopting their three children as a couple. They wanted to do so to protect their parental interests if one of them died.