“They said we could either leave or not listen,” said Ms. Galloway, 51, a therapeutic recreation specialist who has lived here for more than 30 years. “And we felt that was unacceptable.”

Such legislative prayers are far from rare: Both houses of Congress have chaplains, and opening prayers are a feature of many local and state governments. The precedent for such activities is a 1983 Supreme Court decision, Marsh v. Chambers, which allowed state-funded prayers in front of the Nebraska Legislature because the nation’s early leaders had embraced such speech, something also cited by current supporters of the Greece board.

“This has been an unbroken practice in our country for well over 200 years,” said David Cortman, the director of litigation for Alliance Defending Freedom, a Christian-affiliated legal organization that is representing the town.

But lawyers for Ms. Galloway, who is Jewish, and Ms. Stephens, an atheist, say the prayers in Greece “differ in fundamental ways” from those in the Marsh case. They say that the prayers are directed at citizens, not legislators, and that they are not inclusive.

Between 1999 and 2007, all speakers who recited prayers at Town Board meetings in Greece were Christian clergy members, and over the last two years, according to town records, almost all of the prayers have been delivered by either a pastor, deacon or nun. The speakers, facing the crowd and standing at a lectern with a town seal, have repeatedly mentioned Christ, the Holy Spirit and “our Savior”; Bible verses and the Lord’s Prayer have been recited, with the board members sometimes bowing their heads and ending with a chorus of “amen.”