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The Liberty Institute, which held a rally and news conference at the site of the 29-foot cross, will challenge the ruling issued by justices of the 9th U.S. Court of Appeal.

The land underneath the cross -- part of a memorial originally dedicated to those killed in the Korean War -- has been under federal control since 2006.

The foundation's petition to have the high court overturn the appellate justices, who found the cross violated the Establishment Clause of the First Amendment of the U.S. Constitution, stated it is a "fully integrated" part of the memorial and a "passive display" of the sort the high court justices have upheld in the past.

The document said the Supreme Court has previously ruled that displays with religious content don't necessarily violate the Establishment Clause.

Opponents, who also held a news conference and demonstration at the memorial, say the cross unconstitutionally favors a religion while on federal property.

"This cross, which is on government and public land, has no function except to promote one brand of religion," said Bruce Gleason, who belongs to an Orange County group called Backyard Skeptics.

"The defenders of keeping the cross say that the cross is a war memorial, but it was not until a lawsuit against the cross for 1st Amendment violation did the defenders start promoting it as a war memorial."

Last month, the U.S. House of Representatives passed by voice vote a bill by San Diego's Republican congressional delegation to protect religious symbols on war memorials.

The bill still has to go through the Senate and be signed by President Barack Obama before it becomes law.

The foundation said there are thousands of crosses and other religious symbols at veterans memorials throughout the country.

"There is a pressing national need for the court to make clear that memorials adorned with religious symbols such as a cross or the Star of David are not constitutionally suspect," the foundation lawyers wrote.