WASHINGTON — Pivotal Justice Anthony Kennedy, whose vote could decide the same-sex marriage issue for the nation, did not tip his hand Tuesday in historic arguments at the Supreme Court. But Kennedy’s record on the issue could give encouragement to gay and lesbian couples.

As advocates and protesters demonstrated outside, the author of the court’s three prior gay rights rulings talked about the touchstones of dignity and concern for children in same-sex households that drove his favorable earlier opinions.

But he also worried about changing the definition of marriage from the union of a man and a woman, a meaning that he said has existed for “millennia-plus time.”

“It’s very difficult for the court to say ‘We know better’” after barely a decade of experience with same-sex marriage in the United States, Kennedy told Mary Bonauto, a lawyer representing same-sex couples.

The 78-year-old justice’s likely role as a key, perhaps decisive vote was reinforced during arguments that lasted 2½ hours in a rapt courtroom and appeared to divide the court’s liberal and conservative justices over whether the Constitution gives same-sex couples the right to marry. Those couples can do so now in 36 states and the District of Columbia, and the court is weighing whether gay and lesbian unions should be allowed in all 50 states.

“Same-sex couples say, of course, ‘We understand the nobility and the sacredness of marriage. We know we can’t procreate, but we want the other attributes of it in order to show that we, too, have a dignity that can be fulfilled,’” Kennedy said in an exchange with lawyer John Bursch, who was defending the state marriage bans

Later, Kennedy also seemed concerned about adopted children in same-sex households if only one partner is considered a parent. “Under your view, it would be very difficult for same-sex couples to adopt those children,” Kennedy said.

Tuesday’s arguments offered the first public indication of where the justices stand in the dispute over whether states can continue defining marriage as the union of a man and a woman, or whether the Constitution gives gay and lesbian couples the right to marry. In the court’s last look at same-sex marriage in 2013, the justices struck down part of the federal anti-gay marriage law. Federal courts with few exceptions have relied on Kennedy’s opinion in that case to invalidate gay marriage bans in state after state.

The court divided 5-4 in that case, with the liberals joining Kennedy in the majority. Their questions on Tuesday suggested they would vote to extend same-sex marriage nationwide, while conservative justices’ questions and comments were much more skeptical.

Justices Stephen Breyer and Sonia Sotomayor both said marriage was a fundamental right and a state would need a truly compelling reason to deny it to a class of people. Justice Ruth Bader Ginsburg said heterosexual couples would retain the same marriage benefits they currently have, whether or not same-sex couples also could marry.

Bursch argued repeatedly that states could prohibit same-sex unions because marriage always has been about biological bonds between parents and their children.

Justice Elena Kagan said some people have difficulty with that argument, finding it “hard to see how permitting samesex marriage discourages people from being bonded with their biological children.”

If the definition of marriage is changed, Bursch said, “then adults could think, rightly, that this relationship is more about adults and not about the kids.”

The actual cases before the court involve same-sex couples in which both partners want recognition as adoptive parents. In one case, Detroit-area nurses April DeBoer and Jayne Rowse are seeking joint adoption of their four children, and Bursch was quick to say he was not talking about them.

“We all agree that they are bonded to their kids and have their best interest at heart,” he said.

Most of the questions from conservative justices appeared skeptical of gay-marriage arguments.

Chief Justice Roberts said gay couples seeking to marry are not seeking to join the institution of marriage. “You’re seeking to change what the institution is,” he said to Bonauto.

Roberts also said people would be more accepting of change achieved through the democratic process, rather than imposed by courts. Only 11 states have granted marriage rights to same-sex couples through the ballot or the legislature. Court rulings are responsible for all the others.

Yet the chief justice also questioned the states’ argument.

“If Sue loves Joe and Tom loves Joe, Sue can marry him and Tom can’t. Why isn’t that a straightforward question of sexual discrimination?” he asked.