(CNN) -- A federal appeals court decided Tuesday to continue the stay of a judge's ruling that struck down Michigan's same-sex marriage ban, meaning that gay and lesbian couples cannot marry in the state while the appeals process unfolds.

U.S. District Judge Bernard Friedman issued an order Friday that invalidated a state constitutional amendment restricting marriage to between one man and one woman because, in his view, it violated the U.S. Constitution.

His ruling set the stage for same-sex couples to marry immediately. And scores of them did Saturday until the 6th U.S. Circuit Court of Appeals -- after a request filed by Michigan Attorney General Bill Schuette -- issued an order to temporarily stay, or put on hold, Friedman's decision through at least Wednesday.

The same federal court decided to act even sooner than that with its decision Tuesday.

It cited an apparently unanimous Supreme Court order from January regarding a similar case in Utah. Utah had asked the high court to intervene last week after 10th U.S. Circuit Court of Appeals declined to stay a lower court ruling in December striking down Utah's voter-approved prohibition of legal wedlock for gays and lesbians.

Two 6th Circuit appeals judges signed onto Tuesday's decision, making it binding, while one -- Judge Helene White -- dissented. White said that while the Supreme Court did act regarding Utah, "it did so without a statement of reasons, and therefore the order provides little guidance."

Voters in Utah, Michigan and nine other states passed constitutional amendments in 2004 defining marriage as one man and one woman.

Whether same-sex couples should be allowed to wed was a hot-button issue then and in subsequent years, with polls showing that most Americans favored restrictions.

But public opinion shifted over time. An ABC News/Washington Post survey released earlier this month found that 59% of Americans favor allowing gay or lesbian couples to legally wed.

The courts have stepped in as well, most notably the Supreme Court's landmark decision last June rejecting parts of the Defense of Marriage Act while ruling same-sex spouses legally married in a state may receive federal benefits.

Friedman's ruling was the latest in a series of recent similar decisions affecting marriage restrictions in states including Texas, Virginia, Kentucky and Oklahoma. In most all those cases, the judge's orders did not take effect immediately.

But Michigan's did and, as in Utah, scores of same-sex couples sought and got marriage licenses before later court decisions halted such unions -- at least for now, as higher courts weigh in.

In Ingham County, Michigan, for examples, 57 gay and lesbian couples got licenses, according to county clerk Barb Byrum.

It's not immediately clear what will happen to these and other couples, including whether they will be recognized as valid in Michigan.