(CNN) -- Utah officials have asked the U.S. Supreme Court to immediately block enforcement of a federal judge's ruling allowing same-sex couples to be legally married in the state.
An emergency appeal was filed on Tuesday with Justice Sonia Sotomayor, who could rule herself or ask the rest of the court to weigh in.
Any action from the high court would be limited and temporary and would not be the final word on the constitutionality of the state's ban on same-sex marriage.
A Denver-based federal appeals court will take up the larger issues on an expedited basis in coming weeks, but in the meantime has allowed those marriages to take place.
Sotomayor told lawyers for a group of gay and lesbian couples who brought the initial legal challenge to respond to the state's latest appeal by noon Friday.
The Supreme Court could then issue an order on the enforcement question.
U.S. District Court Judge Robert Shelby struck down Utah's ban on same-sex marriage on December 20, saying the law conflicted with equal protection and due process guarantees under the U.S. Constitution.
Utah voters approved a law banning same-sex marriage in 2004.
Shelby's ruling drew national attention partly because Utah is viewed as being among the more conservative states and because the U.S. Supreme Court just ruled this past summer on separate issues involving same-sex marriage.
In June, the nation's highest court cleared the way for same-sex marriages in California to resume after it ruled private parties did not have "standing" to defend California's voter-approved ballot measure barring gay and lesbian couples from state-sanctioned wedlock.
The justices also rejected parts of the federal Defense of Marriage Act (DOMA) in a 5-4 decision, concluding same-sex spouses legally married in a state may receive federal benefits such as tax breaks.
In the Utah case, the state argued Tuesday that numerous same-sex marriages "are now occurring" daily in Utah as a result of the district court decision.
"And each one is an affront not only to the interests of the states and its citizens in being able to define marriage through ordinary democratic channels, but also to this (high) court's unique role as final arbiter of the profoundly important question it so carefully preserved" in the DOMA case, the state said.
The federal judge's ruling prompted a rush of same-sex couples to courthouses in Utah where they obtained marriage licenses, despite the state's ongoing legal challenge.
Utah Gov. Gary Herbert had criticized Shelby's ruling, calling him "an activist federal judge."
Shelby, appointed to the bench last year by President Barack Obama, said the state's "current laws deny its gay and lesbian citizens their fundamental right to marry and, in so doing, demean the dignity of these same-sex couples for no rational reason. Accordingly, the court finds that these laws are unconstitutional."
Same-sex marriage is banned by constitutional amendment or state law in: Alabama, Alaska, Arizona, Arkansas, Colorado, Florida, Georgia, Idaho, Indiana, Kansas, Kentucky, Louisiana, Michigan, Mississippi, Missouri, Montana, Nebraska, Nevada, North Carolina, North Dakota, Ohio, Oklahoma, Oregon, Pennsylvania, South Carolina, South Dakota, Tennessee, Texas, Virginia, West Virginia, Wisconsin and Wyoming.
It is legal in 17 other states and the District of Columbia: California, Connecticut, Delaware, Hawaii, Illinois, Iowa, Maine, Maryland, Massachusetts, Minnesota, New Hampshire, New Jersey, New Mexico, New York, Rhode Island, Vermont and Washington.
Sotomayor handles emergency appeals from Utah and other nearby states.
The same-sex marriage case is Herbert v. Kitchen.