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Mr. Laycock argued that the prayers were sectarian and that Greece residents who show up at board meetings because they have business with the town officials are in effect “coerced” into acquiescing with prayers, whatever their personal religious inclinations.

After Justice Samuel Anthony Alito Jr. asked Mr. Laycock to recite a prayer that was nonsectarian, the attorney suggested that a prayer be offered to “the Almighty” or “the Creator.” This suggestion was shot down by Justice Scalia because it could offend “devil worshippers” or atheists.

“I don’t think it’s possible to compose anything that you could call a prayer that will be acceptable to all of these groups,” Justice Alito said.

Mr. Laycock conceded that it might be impossible to treat everyone equally without eliminating prayer entirely, but he argued that is not the real issue with this case.

“This case is about Christians aggressively imposing their faith on other citizens with the power of government. That is not right, and that is not part of the American tradition,” Mr. Laycock said after the arguments.

Justice Kagan suggested that the question was whether public prayer meetings with references to Jesus Christ should be allowed, and that it was a difficult question to answer.

“The court lays down these rules, and everybody thinks that the court is being hostile to religion and people get unhappy and angry,” she said. “And every time the court gets involved in things like this, it seems to make the problem worse rather than better.”

Outside the courthouse, several protesters against legislative prayer held signs reading “I didn’t vote for Jesus,” “Keep your Theocracy off my Democracy” and “Hi Mom, I’m an Atheist.”

Two members of Faith and Action conducted public prayers while the arguments took place inside the Supreme Court building. The Rev. Pat Mahoney, president of the Christian Defense Coalition, and Peggy Nienaber, chief of program for Faith and Action, prayed for each of the Supreme Court justices as they were surrounded and mocked by some of the protesters.

“God, we thank you that this is a country where we can display our beliefs publicly, no matter what those beliefs may be,” Mr. Mahoney said.