WASHINGTON — The justices announced Friday that the court will hear a pair of cases challenging state and federal laws that define marriage as a union of a man and a woman.

One of the cases, from California, could establish or reject a constitutional right to same-sex marriage. The justices also could rule on narrower grounds that would apply only to marriages in California.

The second case, from New York, challenges a federal law that requires the federal government to deny benefits to gay and lesbian couples married in states that allow such unions.

The court’s move comes against the backdrop of a rapid shift in public attitudes about same-sex marriage, with recent polls indicating that a majority of Americans support allowing such unions. After last month’s elections, the number of states authorizing same-sex marriage increased by half, to nine.

The court’s docket is now crowded with cases about the meaning of equality, with the new cases joining others on affirmative action in higher education and the future of the Voting Rights Act of 1965. Decisions in all of those cases are expected by June.

The new California case was filed in 2009 by Theodore B. Olson and David Boies, two lawyers who were on opposite sides in the Supreme Court’s decision in Bush v. Gore, which settled the 2000 presidential election. The suit argued that California’s voters had violated the federal Constitution the previous year when they overrode a decision of the state’s Supreme Court allowing same-sex marriages.

A federal judge in San Francisco agreed, issuing a broad decision that said the Constitution required the state to allow same-sex couples to marry. The decision has been stayed.

A divided three-judge panel of the 9th U.S. Circuit Court of Appeals, also in San Francisco, affirmed the decision. But the majority relied on narrower grounds that seemed calculated to avoid Supreme Court review or, at least, attract the vote of the court’s presumed swing member, Justice Anthony M. Kennedy.

Judge Stephen R. Reinhardt, writing for the majority, relied heavily on a 1996 majority opinion from Kennedy in a case that struck down a Colorado constitutional amendment that banned the passage of laws protecting gay men and lesbians. The voter initiative in California, known as Proposition 8, had done something similar, Reinhardt wrote.

That reasoning, he added, meant that the ruling was confined to California.

“We do not doubt the importance of the more general questions presented to us concerning the rights of same-sex couples to marry, nor do we doubt that these questions will likely be resolved in other states, and for the nation as a whole, by other courts,” he wrote.

“For now,” he said, “it suffices to conclude that the people of California may not, consistent with the federal Constitution, add to their state constitution a provision that has no more practical effect than to strip gays and lesbians of their right to use the official designation that the state and society give to committed relationships, thereby adversely affecting the status and dignity of the members of a disfavored class.”

The Supreme Court has several options. It could reverse it, leaving California’s ban on same-sex marriage in place. It could affirm on the narrower theory, which would allow same-sex marriage in California but not require it elsewhere. Or it could address the broader question of whether the Constitution requires states to allow such marriages.

A plaintiff in the case, Kristin M. Perry, said she hoped the justices would answer yes to that last question. “There is nothing more important,” she said, “than a state ridding itself of discriminatory laws that hurt its citizens every day.”

Brian S. Brown, president of the National Organization for Marriage, said the court should address the broader question but say no. “What’s at stake,” he said, “is whether the Constitution demands a redefinition of marriage and whether states can even vote on this issue.”

The second case the court agreed to hear challenges a part of the Defense of Marriage Act of 1996. Section 3 of the law defines marriage as between only a man and a woman for purposes of more than 1,000 federal laws and programs. (Another part of the law, not before the court, says that states need not recognize same-sex marriages from other states.)

The case concerns two New York City women, Edith Windsor and Thea Clara Spyer, who were married in 2007 in Canada. Spyer died in 2009, and Windsor inherited her property. The 1996 law did not allow the Internal Revenue Service to treat Windsor as a surviving spouse, and she faced a $360,000 tax bill that a spouse in an opposite-sex marriage would not have had to pay.