WASHINGTON — The Obama administration wants the Supreme Court to overturn California’s gay marriage ban, outlining a broad legal argument that could ultimately be applied to other state prohibitions across the country.

The administration’s friend-of-the-court brief, filed Thursday evening, unequivocally calls on the justices to strike down California’s Proposition 8 ballot measure, although it stops short of the soaring rhetoric on marriage equality President Barack Obama expressed in his inaugural address in January. Still, it marks the first time a U.S. president has urged the high court to expand the right of gays and lesbians to wed.

The brief is not legally binding, though the government’s opinion could carry weight with the Supreme Court when it hears oral arguments on Proposition 8 in late March.

California is one of eight states that give gay couples all the benefits of marriage through civil unions or domestic partnership but don’t allow them to wed. The brief argues that in granting same-sex couples those rights, California has already acknowledged that gay relationships bear the same hallmarks as straight ones.

“They establish homes and lives together, support each other financially, share the joys and burdens of raising children, and provide care through illness and comfort at the moment of death,” the administration wrote.

The brief marks the president’s most expansive view of gay marriage and signals that he is moving away from his previous assertion that states should determine their own marriage laws. Obama, a former constitutional law professor, signed off on the administration’s legal argument last week following lengthy discussions with Attorney General Eric Holder and Solicitor General Donald Verrilli.

In a statement following the filing, Holder said “the government seeks to vindicate the defining constitutional ideal of equal treatment under the law.”

Obama’s position, if adopted by the court, would likely result in gay marriage becoming legal in the seven other states: Delaware, Hawaii, Illinois, Nevada, New Jersey, Oregon and Rhode Island.

In the longer term, the administration urges the justices to subject laws that discriminate on sexual orientation to more rigorous review than usual, as is the case for claims that laws discriminate on the basis of race, sex and other factors.

The Supreme Court has never given gay Americans the special protection it has afforded women and minorities. If it endorses such an approach in the gay marriage cases, same-sex marriage bans around the country could be imperiled.

Despite the potentially wide-ranging implications of the administration’s brief, it still falls short of what gay rights advocates and the attorneys who will argue against Proposition 8 had hoped for. Those parties had pressed the president to urge the Supreme Court to not only overturn California’s ban, but also declare all gay marriage bans unconstitutional.

Still, marriage equality advocates publicly welcomed the president’s legal positioning.

“Obama again asserted a bold claim of full equality for gay Americans, this time in a legal brief,” said Richard Socarides, an attorney and advocate. “If its full weight and reasoning are accepted by the Supreme Court, all anti-gay marriage state constitutional amendments will fall, and quickly.”

The National Organization for Marriage, a leading supporter of the California ban, rejected Obama’s arguments. Spokesman Thomas Peters said he expects the Supreme Court to uphold the votes of more than 7 million Californians to protect marriage, spokesman Thomas Peters said.

The president raised expectations that he would back a broad brief during his inaugural address on Jan. 21. He said the nation’s journey “is not complete until our gay brothers and sisters are treated like anyone else under the law.”

“For if we are truly created equal, than surely the love we commit to one another must be equal as well,” he added.

Obama has a complicated history on gay marriage. As a presidential candidate in 2008, he opposed the California ban but didn’t endorse gay marriage. He later said his personal views on gay marriage were “evolving.”

When he ran for re-election last year, Obama announced his personal support for same-sex marriage but said marriage was an issue that states, not the federal government, should decide.

Public opinion has shifted in support of gay marriage in recent years.

In May 2008, Gallup found that 56 percent of Americans felt same-sex marriages should not be recognized by the law as valid. By last November, 53 percent felt they should be legally recognized.

Gay marriage supporters see the Supreme Court’s hearing of Proposition 8, as well as a related case on the Defense of Marriage Act, as a potential watershed moment for same-sex unions.

In a well-coordinated effort, opponents of the California ban flooded the justices with friend-of-the-court briefs in recent days.

Among those filing briefs were 13 states, including four that do not now permit gay couples to wed, and more than 100 prominent Republicans, including GOP presidential candidate Jon Huntsman and Florida Rep. Ileana Ros-Lehtinen.

Two professional football players who have been outspoken gay rights advocates also filed a brief in the California case. Minnesota Vikings punter Chris Kluwe and Baltimore Ravens linebacker Brendon Ayanbadejo urged the court to rule in favor of same-sex marriage.

The Supreme Court has several options to decide the case that would be narrower than what the administration is asking. The justices also could uphold the California provision, as opponents of gay marriage are urging.

One day after the Supreme Court hears the California case, the justices will hear arguments on provisions of the federal Defense of Marriage Act, which defines marriage as between a man and a woman for the purpose of deciding who can receive a range of federal benefits.

The administration abandoned its defense of the act in 2011, but the measure will continue to be federal law unless it is struck down or repealed.

In a brief filed last week, the government said Section 3 of the act “violates the fundamental constitutional guarantee of equal protection” because it denies legally married same-sex couples many federal benefits that are available only to legally married heterosexual couples.