The Supreme Court wrestled Wednesday with the appropriate role for religion in government in a case involving mainly Christian prayers at the start of a New York town's council meetings.

The justices began their day with the marshal's customary plea that "God save the United States and this honorable court." They then plunged into a lively give-and-take that highlighted the sensitive nature of offering religious invocations in public proceedings that don't appeal to everyone and governments' efforts to police the practice.

The court is weighing a federal appeals court ruling that said the Rochester suburb of Greece, N.Y., violated the Constitution because nearly every prayer in an 11-year span was overtly Christian.

The tenor of the argument indicated the justices would not agree with the appellate ruling. But it was not clear what decision they might come to instead.

Justice Elena Kagan summed up the difficult task before the court when she noted that "every time the court gets involved in things like this, it seems to make the problem worse rather than better."

The justices tried out several approaches to the issue, including one suggested by the two Greece residents who sued over the prayers to eliminate explicit references to any religion.