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The federal government is not a party to the case, Hollingsworth v. Perry, No. 12-144, and was not required to take a position in it. But the lawyers who filed the challenge, Theodore B. Olson and David Boies, along with gay rights groups, lobbied hard for the brief, saying the administration could not stay silent on the issue.

The administration is expected to file the brief Thursday.

The broad outlines of the administration's position were not a surprise, given that it filed a brief last week in a same-sex marriage case in which it is a party, United States v. Windsor, No. 12-307. But that case presents only the narrower question of the constitutionality of part of the federal Defense of Marriage Act of 1996, which defines marriage as the union of a man and a woman for the purposes of more than 1,000 federal laws and regulations.

The Supreme Court's ruling in the Defense of Marriage Act case will at most decide whether the federal government can discriminate against same-sex couples even if they married in states that allow such unions. Nine states and the District of Columbia allow same-sex marriage.

The case from California presents the broader question of whether there is a constitutional right to same-sex marriage in the states that do not allow it, which is why the new brief is significant. It is hardly certain, however, that the Supreme Court will end up deciding that broad question. The court may well avoid the issue on technical grounds or rule in a way that applies only to California.

Until not long ago, the administration was thought likely to stay out of the California case, partly as a matter of historical practice and partly to be true to President Obama's public position on same-sex marriage.

The federal government took no position in 1967 in Loving v. Virginia, the case in which the Supreme Court struck down bans on interracial marriage, or in 2003 in the last major gay rights case, Lawrence v. Texas, which struck down state laws making gay sex a crime.

Moreover, when Mr. Obama announced his support for same-sex marriage, he said the matter was for the states to decide.

"I continue to believe," he told Robin Roberts of ABC News, "that this is an issue that is going to be worked out at the local level, because historically, this has not been a federal issue, what's recognized as a marriage."

That statement is not hard to reconcile with the administration's position in the case concerning the 1996 federal law. As Mr. Obama said in May, the law "tried to federalize what has historically been state law." But the views Mr. Obama expressed in May are in tension with the position taken by his lawyers in the new brief, which calls for federal intervention to override a state law.

(A second part of the 1996 law, which says states need not recognize same-sex marriages performed elsewhere, is not before the Supreme Court.)

On the other hand, Mr. Obama has long opposed Proposition 8, the 2008 California voter initiative that amended the state's Constitution to overturn a State Supreme Court decision establishing a right to same-sex marriage.

"I am not in favor of gay marriage," Mr. Obama told MTV News in 2008. "But when you start playing around with constitutions, just to prohibit somebody who cares about another person, it just seems to me that's not what America's about. Usually, our constitutions expand liberties, they don't contract them."

More recently, Mr. Obama has embraced a more sweeping view of marriage equality.

"Our journey is not complete until our gay brothers and sisters are treated like anyone else under the law," he said in January in his Inaugural Address, "for if we are truly created equal, then surely the love we commit to one another must be equal, as well."

The new brief argues that courts should subject laws making distinctions between straight and gay people to "heightened scrutiny," requiring a showing that such laws are "substantially related to an important government objective." The Supreme Court has never ruled on whether sexual orientation should require such review, but the federal appeals court in New York, in the Windsor case, said that it did.

The administration argues that the factors that led courts to require heightened scrutiny for laws concerning gender and illegitimacy should also require it for those addressing sexual orientation. Gay men and lesbians, the brief said, have suffered a history of discrimination, have distinguishing characteristics and lack political power.

The California case is scheduled to be argued on March 26 and the one concerning the federal law on March 27. Solicitor General Donald B. Verrilli Jr. will probably present the federal government's position in both cases, and he is likely to be questioned closely about changes and possible inconsistencies in the administration's position.