The justices will take up gay-rights cases that ask them to overturn bans in four states and declare for the entire nation that people can marry the partners of their choice, regardless of gender. The cases will be argued in April, and a decision is expected by late June.

Proponents of same-sex marriage said they expect the court to settle the matter once and for all with a decision that invalidates state provisions that limit marriage to opposite-sex couples.

“We are now that much closer to being fully recognized as a family, and we are thrilled,” said April DeBoer, a hospital nurse from Hazel Park, Mich., after the justices said they would hear an appeal from DeBoer and partner Jayne Rowse. “This opportunity for our case to be heard by the Supreme Court gives us and families like ours so much reason to be hopeful.”

Attorney General Eric Holder said the Obama administration would urge the court “to make marriage equality a reality for all Americans.”

On the other side, advocates for traditional marriage want the court to let the political process play out, rather than have judges order states to allow same-sex couples to marry.

“The people of every state should remain free to affirm marriage as the union of a man and a woman in their laws,” said Austin R. Nimocks, senior counsel for the anti-gay marriage group Alliance Defending Freedom.

Same-sex couples can marry in 36 states and the District of Columbia. That number is nearly double what it was just three months ago, when the justices initially declined to hear gay marriage appeals from five states seeking to preserve their bans on same-sex marriage. The effect of the court’s action in October was to make final several pro-gay rights rulings in the lower courts.

Now there are just 14 states in which same-sex couples cannot wed. The court’s decision to get involved is another marker of the rapid change that has redefined societal norms in the space of a generation.

The court will be weighing in on major gay rights issues for the fourth time in in 27 years. In the first of those, in 1986, the court upheld Georgia’s anti-sodomy law. But the three subsequent rulings, all written by Justice Anthony Kennedy, were major victories for gay men and lesbians. In its most recent case in 2013, the court struck down part of a federal anti-gay marriage law in a decision that has paved the way for a wave of lower court rulings across the country in favor of same-sex marriage rights.

James Esseks, leader of the American Civil Liberties Union’s same-sex marriage efforts, recalled the first same-sex marriage case that came to the court more than 40 years ago from Minnesota. There, the justices dismissed a gay couple’s appeal in a single sentence.

“It did not go well because the country wasn’t ready yet. But the country is ready for the freedom to marry today,” Esseks said.

The court is more than doubling the time it usually allots for arguments. The justices will consider two related questions: whether the Constitution requires states to issue marriage licenses to same-sex couples and whether states must recognize same-sex marriages performed elsewhere.

The appeals before the court come from gay and lesbian plaintiffs in Kentucky, Michigan, Ohio and Tennessee. The Cincinnati-based federal appeals court that oversees those four states upheld their same-sex marriage bans in November, reversing pro-gay rights rulings of federal judges in lower courts. It was the first, and so far only, appellate court to rule against same-sex marriage since the high court’s 2013 decision.

One of the plaintiffs from Ohio, James Obergefell, said he was crying “tears of joy and sadness” after the court accepted his appeal. In 2013, Obergefell flew to Maryland with his dying partner, John Arthur, so they could marry before Arthur’s death. The couple sued to force Ohio to list Arthur as married on his death certificate, which would allow the men to be buried next to each other. Obergefell died 15 months ago.

“I can’t wait to walk up those steps and have the Supreme Court understand that we’re just like everyone else,” Obergefell said.