WASHINGTON – In the opening day of oral arguments for two historic gay marriage cases, Supreme Court justices wrestled with the questions of whether marriage itself is an institution defined by a couple’s sex and tied to producing children, and whether redefining it could lead to societal harm.

The nation’s highest court Tuesday also questioned whether nine justices should weigh in on an issue on which public opinion is shifting rapidly, even as they heard a challenge to California’s voter-approved 2008 ban of same-sex marriages.

The closely watched arguments could prompt the court to establish the constitutional right for gays to marry in all states.

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Or the court could do nothing at all. As a legal matter, striking down the California ban would take the Supreme Court into ``uncharted waters,’’ said Justice Anthony Kennedy, raising the question whether the court may find itself uncomforable inserting itself into the volatile social issue.

Charles Cooper, the attorney arguing on behalf of gay marriage opponents, said marriage between a man and a woman is in the best interest of society because only such a union could lead to “responsible procreation.” Since gay couples do not have the biological capacity to produce children together, the equal protection clause under the constitution does not apply to them, he argued.

In a spirited debate over the purpose of marriage, Justice Elena Kagan compared denying gays and lesbians the right to marry with denying couples over age 55 a marriage license simply because of their slim chances of bearing children.

Justice Ruth Bader Ginsburg asked why a prisoner, locked behind bars with no possibility of procreating, should then have a right to marry.

Voters in California banned gay marriage six months after the state Supreme Court endorsed such unions. Proposition 8 amended the state’s constitution to only recognize marriages between a man and a woman. Lower courts had declared the gay marriage ban to be unconstitutional.

Theodore Olson, the attorney for the two California couples challenging the ban, said the amendment unfairly discriminates against gays and lesbians by walling them off from the institution of marriage, which he argues is an individual right. Procreation is not a fundamental part of marriage, he said.

Heterosexual couples have always been allowed to marry whether or not they intend to have children. And gay couples have become parents through adoption, surrogacy and artificial insemination.

Olson tangled with Justice Antonin Scalia who challenged him repeatedly to answer his question of when it became unconstitutional to prohibit homosexuals from marrying. Scalia asked him whether the case would still stand if the California amendment known as Proposition 8 were enacted before the court allowed gay marriage.

Solicitor General Donald Verrilli, Jr. also urged that the California ban be struck down because the state has already extended all substantive rights and responsibilities of marriage to gay and lesbian domestic partners. That reasoning also results in the Constitution requiring marriage equality in seven other states that recognize domestic partner rights.

The significance of the case will ultimately depend on how the court rules. The court could reverse the lower-court decision and let the state ban stand, or it could uphold the decision and end the ban in California. It could also declare all state bans against gay marriage to be unconstitutional.

Massachusetts became the first state to legalize gay marriage in 2003. Eight other states, plus the District of Columbia, have followed suit. But 31 states have bans against it.

Public support for gay marriage has grown to an all-time high of 58 percent, according to a Washington Post-ABC News poll published last week. That is a dramatic flip from 2010 when more people opposed same-sex marriage than supported it.

Gay marriage supporters and others intent on witnessing history slept in line outside the Supreme Court for five days, through rain and snow. This morning they gathered their folding chairs and sleeping bags, and the first 50 were ushered inside the court room.

Others spent the night with no hopes of claiming a coveted public seat. Instead, they secured prominent posts in front of the courthouse steps, holding signs promoting marriage equality along with rainbow flags and American flags.

“There is no where else I’d rather be,” said J. Mary Sorrell, who says she became Massachusetts’ first openly lesbian justice of the peace in 2004 and has officiated the weddings of numerous gay couples from around the world. “This is the civil rights issue of our day, and I don’t take it for granted.”

Sorrell, of Haydenville, Massachusetts, said that when gay marriage was allowed in Massachusetts, “I could feel there would be reverberations way beyond our little Commonwealth. But I didn’t think that just nine years later we’d be here at the Supreme Court oral arguments.”

Sara Conklin, a 23-year-old from Jacksonville, Fla. who works for the Human Rights Campaign in Washington, spent the night in front of the court with 50 others from her coalition to claim a broad swath of space for a rally that is expected to draw 10,000 people today.

“We need a lot of bodies here showing support,” Conklin said. “The fact that Proposition 8 happened is an embarrassment to the state of California.”

Linda Sanderson, 44, of Rockville, Maryland, came alone, holding a banner emblazoned with a pair of wedding rings and a rainbow.

“I just hope the Supreme Court decides on the right side of justice,” said Sanderson, who hails from Michigan but fled the state with her partner, a teacher, after voters decided against benefits for domestic partners. “I think they need to mind their own business, with all due respect.”

Opponents of gay marriage were not visible in front of the Supreme Court on Tuesday morning.

On Wednesday the court will hear a challenge to the 1996 Defense of Marriage Act, which bars married gay couples from receiving federal marriage benefits such as spousal disability, Social Security and family medical leave. The federal law defines marriage as a union between one man and one woman. President Clinton, who signed the law, recently recommended that it be overturned.

A Gallup poll two weeks ago found that the majority of Americans – 54 percent – would vote for a law conferring marriage benefits such as those for insurance, taxes or Social Security to spouses of federal employees in same-sex marriages. Only 39 percent said they would vote against such a law.

President Obama, who last May became the first president to announce his support for gay marriage, has said he think the law is unconstitutional and his administration has declined to defend it. He again championed the right of gays to marry in his inaugural address in January.

The court is expected to hand down decisions in both cases in June.

“The court has a really important role here and its job is to protect minorities,” said Ara Gershengorn, partner with the Boston-based law firm Foley Hoag and the co-author of an amicus brief filed on behalf of former cabinet secretaries and other senior administration officials who are against the Defense of Marriage Act.

“It may be that the political process will get there,” Gershengorn said, referring to growing popular support for gay marriage. “But the job of the court is to determine if this is violating the constitutional rights of these individuals today.”