The justices turned aside an appeal by the city of Elkhart, Indiana. The city had argued that the monument, which contains the text of the Ten Commandments as part of a larger civil display, did not violate church-state separation under the First Amendment.
The Supreme Court action, in denying the appeal, does not set a national precedent.
The monument has stood on the lawn outside of Elkhart´s City Hall since its donation by the Fraternal Order of Eagles, a service organization, in 1958 as part of a national program.
The city defended the monument as a historical artifact and one of a number of displays across the country depicting America´s heritage.
Two Elkhart residents, represented by the Indiana Civil Liberties Union, sued the city in 1998 to get rid of the monument near the building´s main entrance.