WASHINGTON — The Supreme Court said this morning it will hear a new case on the intersection of religion and government in a dispute over prayers used to open public meetings.

The justices said they will review an appeals court ruling that held that the town of Greece in suburban Rochester in upstate New York violated the Constitution by opening nearly every meeting over an 11-year span with prayers that stressed Christianity.

The 2nd U.S. Circuit Court of Appeals said the town should have made a greater effort to invite people from other faiths to open its monthly board meetings.

The town says the high court already has upheld prayers at the start of legislative meetings and that private citizens offered invocations of their own choosing. The town said in court papers that the opening prayers should be found to be constitutional, “so long as the government does not act with improper motive in selecting prayer-givers.”

Two town residents who are not Christian complained that they felt marginalized by the steady stream of Christian prayers and challenged the practice. They are represented by Americans United for Separation of Church and State.

Reacting to the court action Monday, the Rev. Barry W. Lynn, Americans United executive director, said, “A town council meeting isn’t a church service, and it shouldn’t seem like one.”

From 1999 through 2007, and again from January 2009 through June 2010, every meeting was opened with a Christian-oriented invocation. In 2008, after residents Susan Galloway and Linda Stephens complained, four of 12 meetings were opened by non-Christians, including a Jewish layman, a Wiccan priestess and the chairman of the Baha’i congregation.

Arguments will take place in the fall.