Its attorney general's office filed an emergency request to stay a decision by judge Robert J. Shelby of Utah's Federal District Court, who said the state's law conflicts with the US constitution.
"Applicants respectfully apply for an immediate stay pending an appeal of a judgment and injunction ... invalidating .. Utah's marriage laws," said the 101-page legal document, posted on the attorney general's website.
On December 20 judge Shelby struck down Utah's gay marriage ban -- approved by voters in a referendum in 2004 -- saying it violated the right of same-sex couples to equal protection under the 14th Amendment to the constitution.
Opponents of gay marriage appealed, but their initial attempt to have the ruling suspended was rejected.
Tuesday's New Year's Eve appeal was made initially to US Supreme Court Justice Sonia Sotomayor, who oversees such emergency applications to the United States' top court in Washington DC.
Marriage laws are governed by individual US states, nearly 30 of which have amended their constitutions to ban same-sex marriage.
Efforts to give same-sex couples the same rights as heterosexuals have gathered steam in recent years.
One of the most important victories came in June when the US Supreme Court struck down the Defense of Marriage Act, which defined marriage as a union between one man and one woman.
Seventeen US states and the federal capital Washington DC have so far legalized same-sex marriage, including New Mexico earlier in December.
The other states are: California, Connecticut, Delaware, Hawaii, Illinois, Iowa, Maine, Maryland, Massachusetts, Minnesota, New Hampshire, New Jersey, New York, Rhode Island, Vermont and Washington.