Joining the Utah-based Church of Jesus Christ of Latter-day Saints in its appeal to the court are 18 other religious and religious groups including Assemblies of God, Southern Baptist Convention, Free Methodist Church, Lutheran Church-Missouri Synod, the National Association of Evangelicals and the Christian Legal Society.
"Not withstanding our theological differences, we are united in declaring that the traditional institution of marriage is indispensable to the welfare of the American family and society," the document states. "We are also united in our belief that a decision requiring the states to license or recognize same-sex marriage would generate church-state conflicts that will imperil vital religious liberties."
In a statement, Mormon church spokesman Eric Hawkins characterized the faith's partnership with other religions in filing the brief as an extension of its deep and well-documented commitment to traditional marriage.
"We believe that a redefinition of marriage to include same–sex couples has profoundly troubling implications for society in the long term," Hawkins said.
"We have therefore joined with many other diverse faiths representing tens of millions of Americans in expressing our views to the Supreme Court."
The church's position is not unexpected. Mormon leaders have been consistently politically active in efforts to ban gay marriage across the U.S. since the 1990s and lobbied Congress for a constitutional amendment to protect marriage between one man and one woman in 2004.
The filing comes a little more than a month after LDS leaders worked alongside Utah's lesbian, gay, bisexual and transgender community to pass a historic statewide law to prevent discrimination against LGBT individuals in housing and employment. The legislation also included exemptions for churches and their affiliates and provides some protections for individuals.
A Monday post on the church's website seeks to explain why church leaders would support nondiscrimination and oppose same-sex marriage.
"The legalization of same-sex marriage across the country does far more than grant same-sex couples the right to the same benefits as heterosexual married couples," the post, titled "Religious Freedom and Fairness for All," states.
"By redefining what marriage has been for most of human history, the court will impede the ability of religious people to participate fully as equal citizens in American civic life."
The statement adds that the LDS Church does not seek to dictate how others should live their lives, but brings its "values to the public square" and makes its case through the same channels as all.
"We can no more prohibit same-sex partnerships among the general population than we can mandate against heterosexual cohabitation before marriage," church leaders said. "In a pluralistic society, we make space for the rights and opinions of others, persuasively argue for laws that uphold moral principles based on our understanding of the gospel of Jesus Christ and encourage our own members to live by those principles."
Gay marriage is currently legal in most states. Same-sex marriage became legal in Utah in December 2013, when a U.S. District Court judge struck down the state's ban on gay unions as unconstitutional.
The decision was stayed as the state appealed, but Utah lost its case before judges from the 10th U.S. Circuit Court of Appeals in Denver last July.
The state filed a second appeal, to the U.S. Supreme Court, but in October 2014, the high court let stand multiple circuit court rulings that had overturned marriage-equality bans a decision that effectively legalized same-sex marriage in Utah and 10 other states.
The Utah attorney general's office also has filed an amicus brief urging the U.S. Supreme Court to uphold state bans on same-sex marriage. Salt Lake City, Park City and former Utah Gov. Jon Huntsman Jr. joined other organizations in briefs that support gay marriage.