The same-sex marriages performed across the socially conservative state have created chaos, Utah said in a 25-page application to Justice Sonia Sotomayor arguing for a stay of the court's Dec. 20 ruling.
U.S. District Judge Robert J. Shelby in Salt Lake City ruled Utah's definition of marriage as solely between one man and one woman denied same-sex couples the "fundamental right" to civil marriage under the due process and equal protection clauses of the Constitution's 14th Amendment.
Utah's marriage definition was approved by 66 percent of voters in a 2004 referendum amending the state's Constitution.
Sotomayor handles emergency legal applications from Utah and surrounding states in the jurisdiction of the 10th Circuit Court of Appeals, which rejected Utah's three earlier requests to delay Shelby's decision to let lesbian, gay, bisexual and transgender couples marry.
"Numerous" same-sex marriages are performed every day in Utah, said the state's application, cited by the Deseret News in Salt Lake City.
"And each one is an affront not only to the interests of the state and its citizens in being able to define marriage through ordinary democratic channels, but also to this court's unique role as final arbiter for the profoundly important constitutional question it so carefully preserved in Windsor," the state said.
"Windsor" refers to United States vs. Windsor, the case in which the Supreme Court in June overturned part of the U.S. Defense of Marriage Act as an unconstitutional "deprivation of the liberty" protected under the Fifth Amendment's due process clause.
But Utah contends in its argument most justices in the case said states had the power to define marriage, so Utah should be allowed to limit marriage the way it wishes.
"This case involves not just a refusal by the federal government to accommodate a state's definition of marriage, but an outright abrogation of such a definition -- by a single federal court wielding a federal injunction and acting under the banner of the federal Constitution," Utah argued.
Sotomayor could rule on the state's request for a stay, but is expected to refer it to the entire court, the New York Times said.
If that happens, the justices would likely rule within days.
Sotomayor Tuesday ordered the other side in the case -- three gay and lesbian couples who sued to challenge Utah's same-sex marriage ban -- to file their response to Utah's stay request by noon EST Friday.
James Magleby, a lawyer for the gay and lesbian couples, said the state's request lacks merit.
"The 10th Circuit has already established a rare, expedited briefing schedule on these issues, and hundreds of same-sex couples have already been married in Utah. Thus, there is no emergency need for a stay," he said in remarks quoted by the News.
Sotomayor was in New York City's Times Square New Year's Eve to start the midnight ball drop marking the start of the new year.