The Coalition for the Protection of Marriage said the case crystalizes the fundamental question of whether the legal definition of marriage should be changed from a man and a woman to the union of any two people.
The coalition filed documents seeking what is known as a writ of certiorari that asks the Supreme Court to take the case before it can be considered by the 9th U.S. Circuit Court of Appeals in San Francisco.
The Lambda Legal Defense and Education Fund vowed last week to appeal to the 9th Circuit a federal judge's ruling in Reno that Nevada has a "legitimate state interest" in prohibiting the recognition of same-sex couples.
Lambda attorney Tara Borelli, in Los Angeles, said she will oppose the coalition petition and officials with the gay rights organization doubt the Supreme Court will take up the case.
The coalition, based in Boise, Idaho, opposes gay marriage and was involved in the Nevada case. Monte Stewart, a lawyer for the group, declined comment on the effort to have the Supreme Court intervene.
"The fundamental marriage issue is whether ... the legal definition of marriage (should) be changed from the union of a man and a woman to the union of any two persons," the coalition filing said.
In its 127-page filing, the coalition called the Nevada case the clearest among several gay marriage cases the high court could consider because it hinges on that "fundamental" question and isn't encumbered by side issues.
"This case has developed most comprehensively and thoroughly the societal interests justifying preservation of marriage's man-woman meaning," the document said.
The Nevada lawsuit, Sevcik v. Sandoval, was filed in April on behalf of eight Nevada couples. It was the first by Lambda Legal to make the direct state marriage equality claim in federal court.
It said a 2002 state constitutional amendment prohibiting same-sex marriage violated the Equal Protection Clause of the U.S. Constitution by denying same-sex couples in Nevada the same rights that other married couples enjoy.
The lawsuit also accused the state of establishing a "selective bar to access to marriage" with a 2009 domestic partnership law that lets hospital officials and police officers question a same-sex couple's relationship status because they aren't legally recognized as spouses.
Lambda Legal attorney Tara Borelli has said letting domestic partners register their legal status but not marry brands them as "second-class citizens."
Nevada is one of 31 states with a constitutional provision prohibiting same-sex marriage. Nine states have approved gay marriage, including Maine, Maryland and Washington last month. Minnesota voters defeated a proposal to add a gay marriage ban to that state's constitution.
The case in Nevada followed a four-year legal battle in California over that state's Proposition 8 ban on same-sex marriages. That is one of several questions now on the doorstep of the U.S. Supreme Court. Justices also are considering taking up a challenge to part of the federal Defense of Marriage Act of 1996.