The defeat for suspended Alabama Chief Justice Roy Moore was expected.
The court has already taken on one divisive case about government and religion, a challenge to the phrase "one nation under God" in the Pledge of Allegiance.
Moore said he would go state-to-state to keep alive his political crusade for the Ten Commandments, even though justices rejected his final appeals without comment.
Lower federal courts had ruled that Moore violated the Constitution's ban on government promotion of religion when he placed the monument in the rotunda of the state Judicial Building in the middle of the night two years ago. The display was moved this summer over Moore's objections.
"It's not over. We do not intend to be stopped. We do not intend to give up. We have only begun to fight," Moore, who has offered to let Congress use his display in the Capitol, said at a news conference in Alabama.
On the Supreme Court sidewalk, about 10 Moore supporters kneeled and prayed on Monday around Ten Commandment tablets after calling the justices hypocrites and cowards.
The biblical law is represented several places in the Supreme Court's marbled building, including a frieze in the courtroom that depicts Moses holding two tablets with the commandments.
"That is pure elitism and hypocrisy," said the Rev. Rob Schenck, president of the Washington-based National Clergy Council. "If you can display these Ten Commandments above your heads, why can't the people of Alabama display them in the rotunda of their Supreme Court building?"
In appeals to the Supreme Court, Moore argued that lower federal courts do not have authority over a state's chief justice. Moore was suspended as chief justice for defying a federal court order to remove the monument. He goes on trial before the Alabama Court of the Judiciary on Nov. 12 on judicial ethics violation charges.
"Politically this isn't over," said the Rev. Barry W. Lynn, executive director of Americans United for Separation of Church and State, one of the groups that sued over the display. "But this doesn't have the traction that some of the other social issues have for the religious right."
The Supreme Court's action is not a ruling on the thorny question of whether the Ten Commandments may be displayed in government buildings. It merely reflects the high court's unwillingness to hear the appeal.
Lower courts have splintered on the issue, allowing depictions of the Ten Commandments in some instances and not in others.
Moore challenged the high court to settle the question once and for all, and accused the justices of ducking their responsibility to clarify murky questions about the constitutional principle of separation of church and state.
The Constitution sets out no absolute divide between God and government, and Moore argued that his Ten Commandments display was in keeping with the religious vision of the nation's founders.
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