Oklahoma's Supreme Court on Monday said the state must remove a Ten Commandments stone monument first placed at its Capitol in 2012, rejecting an appeal to reconsider an earlier decision.

The justices denied a request by the Oklahoma Capitol Preservation Commission to rethink the court's June 30 decision that the statue's placement violates the state constitution's ban on the use of state property for the benefit of religion.

Earlier in July, Oklahoma Governor Mary Fallin, a Republican, had said she would keep the monument in place while lawmakers sought a way to block the decision.

The 6-foot-tall monument was paid for with private money and is supported by lawmakers in the socially conservative state. Some lawmakers had threatened to impeach the justices or amend the constitution.

"We carefully consider the arguments of the commission and find no merit warranting a grant of rehearing," Chief Justice John Reif wrote.

After the Ten Commandments monument went up, other groups including Satanists and the Church of the Flying Spaghetti Monster applied to erect their own monuments on Capitol grounds to mark what they say are historical events.

The Satanic Temple unveiled its bronze Baphomet sculpture in Detroit on Saturday after failing to have it installed near Oklahoma's Ten Commandments monument.

Jex Blackmore, director of the Satanic Temple Detroit chapter, said members plan to ship the sculpture to Arkansas, where a law authorising a Ten Commandments statue on capitol grounds was approved earlier in 2015.

A spokesman for Fallin said the state has not received a final order to remove the monument, which would come from district court.

"In the meantime, the state is reviewing what legal options are available for preserving the monument," spokesman Alex Weintz said.