The legal battle over whether same-sex couples have a constitutional right to marry came for the first time Thursday before a panel of appeals court judges, who struggled to decode the Supreme Court’s message on gay rights last summer.

In weighing whether Utah’s ban on same-sex marriages withholds a fundamental right that must be made available to all, the three-judge panel of the U.S. Court of Appeals for the 10th Circuit said that the Supreme Court ruling in the U.S. v. Windsor case holds the key.

The Supreme Court’s 5 to 4 decision struck down the federal government’s definition of marriage as only between a man and a woman and said federal authorities must recognize same-sex unions performed in states where they are legal.

But the ruling did not find that states must offer the right and left open exactly how lower courts should decide whether state bans represent a rational protection of the age-old definition of marriage or a form of unconstitutional discrimination.

Appeals courts around the country are set to grapple repeatedly with that issue in the coming months, after a series of recent decisions by federal courts favorable to same-sex marriage. Federal judges in Virginia, Oklahoma, Texas and Michigan have struck down bans in those states. Courts in Tennessee, Ohio and Kentucky have said those states must recognize same-sex marriages performed elsewhere.

In fact, the same three 10th Circuit judges will meet next week to consider the Oklahoma case, and next month, the U.S. Court of Appeals for the 4th Circuit in Richmond will review Norfolk-based U.S. District Judge Arenda L. Wright Allen’s decision striking down Virginia’s laws.

All are in service of returning the issue to the Supreme Court, likely in time for the justices to consider the constitutional question in its term that begins in October.

In Thursday’s arguments, Utah’s attorney, Gene C. Schaerr, acknowledged that an unbroken line of federal judges have ruled that the Windsor decision means the state bans must fall, just as a Salt Lake City judge ruled in Utah.

But Schaerr said the judges were misreading the Supreme Court opinion’s central point that states have the lead in defining marriage and that they should not believe the Supreme Court “with a wink and a nod” was telling lower courts to recognize a constitutional right.

Circuit Judge Paul F. Kelly Jr. seemed inclined to agree with Schaerr that it should be up to Utah residents and legislators to define marriage.

His colleague Carlos Lucero sharply disagreed, saying the state’s justifications for enshrining what Schaerr called the “man-woman model” of marriage were considered and rejected by the Supreme Court when examining Congress’s decision for such a definition in the Defense of Marriage Act.

The third judge, Jerome A. Holmes, seemed torn over what the Supreme Court requires. He gave hope to those who challenged the ban by immediately comparing the case to Loving v. Virginia, the Supreme Court’s 1967 landmark decision striking down bans on interracial marriage.

He pressed Schaerr: How is this different? In Loving, the couple was prevented from marrying only because of race. “Here you have a man who wants to marry another man,” Holmes said. “The only thing that prevents it is gender.”

At the same time, he said, the Supreme Court was unclear about how judges should scrutinize state bans. If a state government must only show it has a rational basis for its decision to enact a ban, it likely wins, he said. If the decision to treat one group differently from another demands more justification than that, the government likely loses, he said.

Utah’s ban, enacted overwhelmingly by voters in 2004, was challenged by two same-sex couples who want to marry — Derek L. Kitchen and Moudi D. Sbeity; and Laurie Wood and Kody Partridge — and by Kate Call and Karen Archer, who married in Iowa and want Utah to recognize their marriage.

U.S. District Judge Robert Shelby became the first judge to strike down a state ban after the Windsor decision when he ruled in their favor in December.

“The state’s current laws deny its gay and lesbian citizens their fundamental right to marry and, in so doing, demean the dignity of these same-sex couples for no rational reason,” Shelby wrote.

Shelby and then a panel of the 10th Circuit — Holmes was a member — turned down Utah’s request to put the decision on hold while it was appealed. More than 1,200 couples were wed before the Supreme Court approved Utah’s stay request 17 days later.

The justices gave no reason for granting the stay and thus shed no more light on the court’s reasoning in Windsor.

In asking the court to be “appropriately deferential to democracy,” Schaerr told Holmes that Loving was a different case because it did not change the definition of marriage as between those of different genders.

He said Utah’s view of marriage is based on what is best for children, and that is being raised with a mother and father. He said those challenging the ban believe marriage is only about adults and their desires.

Schaerr, an experienced appellate lawyer who resigned from his Washington law firm to represent the state, got tough questions from Holmes, who was nominated by President George W. Bush, and Lucero, a choice of President Bill Clinton.

Holmes questioned whether the state had provided any proof that children raised by same-sex couples fared worse than those raised in heterosexual households.

And Lucero questioned how the state promoted its stated goals by prohibiting same-sex marriage.

“How is a heterosexual couple more likely to get married if a gay couple is not allowed to get married?” he asked.

When Schaerr said, more than once, that a view of marriage based only on what adults desire could make it hard to rule against polygamy, Lucero stopped him.

“There’s plenty of time to talk about polygamy. Let’s talk about gay marriage today,” Lucero said.

Lucero was more supportive of lawyer Peggy A. Tomsic, who represented the couples.

Tomsic said deference to democracy does not mean that the majority can curb the constitutional rights of a minority.

But she was pressed by Kelly on the fact that the Supreme Court has not found there is a constitutional right for same-sex couples to marry.

Kelly said that he was not inclined to believe those who voted to put the traditional definition of marriage in the Utah constitution did so because they were mean-spirited or bigots.

“Just because you disagree with the state doesn’t make it irrational, does it?” he asked.

Tomsic said the state had failed to provide any proof for its rationale that same-sex parenting is worse for a child than other households. Even if the state must only prove it has a rational basis for a decision, she said, that standard is not “toothless.”

“When the government separates people into classes for unequal treatment,” Tomsic said, the burden is on the state to prove why.

Utah’s policy on marriage, she said, cannot be reconciled with its stated goals, she said. The state’s ban does not “reaffirm” traditional marriage, she said; “it is to exclude” same-sex couples.

Holmes said Tomsic was right that Utah cannot withhold something that is a constitutional right.

“What we’re trying to determine is, what is the constitutional right?” he said.

It could be months before the 10th Circuit panel rules. Its decision would be binding on the states within its jurisdiction: Colorado, Kansas, New Mexico, Oklahoma, Utah and Wyoming.

But New Mexico’s highest state court already took note of the Windsor decision and ruled unanimously that the state must allow same-sex marriages.