Rev. Patrick Mahoney of the Christian Defense Coalition prays outside the Supreme Court as it hears arguments in the case of Town of Greece, N.Y. v. Galloway on Wednesday. (JAMES LAWLER DUGGAN/REUTERS)

The Supreme Court struggled Wednesday with how the government can accommodate the nation’s religious traditions without endorsing beliefs not shared by all as the justices considered a New York town’s practice of opening its meetings with mostly Christian prayers.

The court decided 30 years ago that legislatures may begin sessions with an invocation. But Wednesday’s oral arguments examined whether there might need to be different rules for a local council meeting, where citizens often come to ask for favorable official action. The arguments also considered whether by opening its session almost always with prayers from one faith, a government essentially identifies itself with that specific religion.

A federal appeals court said the town of Greece, N.Y., had done just that with a decade of mostly Christian prayer.

As always, Wednesday’s court session began with the marshal’s intonation “God save the United States and this honorable court.”

But Justice Elena Kagan, drawing on facts in the case, immediately asked Thomas G. Hungar, the town’s attorney, whether it would have been proper for the court’s session to open a different way: with a minister asking all in attendance to stand and pray with him about “the saving sacrifice of Jesus Christ on the cross.” In this scenario, Kagan continued, “The members of the court who had stood responded ‘Amen,’ made the sign of the cross, and the chief justice then called your case.”

Hungar said he did not think that would be permissible. But he said that courts are different from legislative bodies, and that the “history of this country from its very foundations and founding recognizes the propriety of legislative prayer of the type that was conducted” in the town.

In general, the court’s liberal members seemed most concerned about the town’s practices. Every meeting from 1999 to 2007 opened with a Christian prayer, and even after two of the town’s residents filed a lawsuit, only a handful of non-Christian speakers have delivered the invocation.

Conservatives on the court worried about the potential remedy. Insisting that prayers be “nonsectarian,” they feared, would put government in the position of censoring prayers or stifling religious expression in a way that could also violate the Constitution.

“Who is going to make this determination?” Chief Justice John G. Roberts Jr. asked. “You have to review the proposed prayer?”

Even Kagan, perhaps the justice most critical of Greece’s policy, noted the difficulty.

“Part of what we are trying to do here is to maintain a multi-religious society in a peaceful and harmonious way,” she said. “And every time the court gets involved in things like this, it seems to make the problem worse rather than better.”

Kagan and Justice Ruth Bader Ginsburg wondered about the difference between legislative bodies such as Congress, where the audience members are spectators, and a town council, where citizens sometimes are compelled to attend to receive specific recognition or make requests.

Douglas Laycock, a University of Virginia law professor representing the complaining residents, Susan Galloway and Linda Stephens, said that is what distinguished the case from the court’s landmark 1983 decision in Marsh v. Chambers. That ruling said Nebraska had not violated the Constitution by employing a Presbyterian minister for 16 years to lead the legislature in prayer.

Laycock said Greece’s practice forced citizens who might not agree with the prayer to either participate against their will or irritate council members from whom they hoped to receive favorable action.

He said that the town should be allowed to offer prayers, but that those prayers should “stay away from points on which believers disagree.”

Justice Samuel A. Alito Jr. told Laycock that in a country as religiously diverse as this one, “I just don’t see how it is possible to compose anything that you could call a prayer that is acceptable to all of these groups.”

On the other side of the issue, Justice Antonin Scalia said that town council members have a right to call on divine guidance.

“The people who are on the town board or the representatives who are in Congress, they’re citizens,” not judges, he said, adding, “These people perhaps invoke the deity at meals. They should not be able to invoke it before they undertake a serious governmental task such as enacting laws or ordinances?”

Of course they may, Laycock said, but they could do it silently, or before the meeting.

Justice Anthony M. Kennedy — who generally has favored religious activity in the public square but drawn the line at government actions that would compel an individual to participate in religious observance — did not seem convinced by Hungar or Laycock, or by the arguments of Deputy Solicitor General Ian H. Gershengorn on behalf of the federal government, which is supporting the town.

He told Hungar that his argument simply amounted to “We’ve always done it this way.”

But he worried that Laycock’s proposal “involves the state very heavily in the censorship and the approval or disapproval of prayers.”

Justice Stephen G. Breyer seemed to be devoted to finding a middle ground.

The council, which previously opened its meetings with a moment of silence, drew its volunteer chaplains from a list of churches in the town. It said that anyone would have been welcomed but that it did not publicize the opportunity. The council neither created rules for the prayers nor screened them beforehand.

One thing the town could do, Breyer said, is “make a good-faith effort to appeal to other religions who are in that area.”

The town need not suggest prayers or edit them, he said, but could try to make them more inclusive. He suggested wording from the House: “The chaplain should keep in mind that the House of Representatives, or you would say whatever relative group, ‘is comprised of members of many different faith traditions,’ period, end of matter.”

The case is Town of Greece v. Galloway .