Washington (CNN) -- A war memorial shaped like a cross that has been at the center of a Supreme Court fight has been torn down by vandals from its remote perch in a California desert.

The 6-foot-tall metal structure was removed Sunday night from Sunrise Rock in a lonely stretch of the Mojave National Preserve, said government officials and veterans groups that have been fighting for years to keep the cross on national park land.

The National Park Service said it is investigating the incident; no arrests had been made as of Tuesday morning.

The high court on April 28 ruled the cross did not violate the constitutional separation of church and state. The American Civil Liberties Union, which had brought the original lawsuit to have the cross removed, promised to continue the court fight.

The Veterans of Foreign Wars and the Liberty Institute, the legal organization that represents the veterans groups in the case, are offering rewards totaling $35,000 for information leading to the arrest and conviction of those behind the theft.

"This is an outrage, akin to desecrating people's graves," said Kelly Shackelford, president and CEO of Liberty Institute. "It's a disgraceful attack on the selfless sacrifice of our veterans. We will not rest until this memorial is re-installed."

The Latin cross was first erected in 1934 by a local VFW unit to honor war dead. It has been rebuilt several times over the years, and Easter services are held annually at the remote desert site. The site is on national park land that totals about 1.6 million acres, or 2,500 square miles.

The cross itself was embedded in rock held in place by concrete. Whomever removed it would have had to climb up the steep outcropping, maneuvering around rattlesnakes that hide in the crevices.

A federal judge in 2001 ordered the cross covered with plywood until the legal issues were resolved. Many tourists driving by the site had believed the memorial was a neglected billboard.

The Park Service told CNN the wooden cover was reported missing Saturday morning. When staff arrived Monday to replace it, the cross itself was missing.

"Park law enforcement is investigating this crime and is asking for the public's assistance," said Linda Slater, a Mojave National Preserve spokeswoman.

The unofficial caretakers of the structure said they are heartbroken at its disappearance. Henry and Wanda Sandoz have driven 140 miles each way from their home on a weekly basis to maintain the area. Sitting near the cross last September, Henry Sandoz told CNN he has done heavy maintenance over the years.

"Up until the box went on it, I would replace it when it got knocked down, repair it," he said. "The last time, I had to get a couple of cowboys across the way and they helped me put it up. We had to literally to hoist it up because it's heavy, 3-inch pipe, and filled it with cement. I put it up to stay."

Frank Buono, a former Park Service employee, initiated the lawsuit, saying the cross represented government endorsement of the Christian faith. A federal appeals court ultimately agreed, and rejected a move by Congress in 2003 to transfer the tiny portion of land where the cross sits to the VFW as a privately held national memorial.

The justices did not completely resolve the fight over the fate of the cross, but the conservative majority re-affirmed recent rulings that there is a limited place for religious symbols on government land.

"It is reasonable to interpret the congressional designation as giving recognition to the historical meaning that the cross had attained," wrote Justice Anthony Kennedy. "The Constitution does not oblige government to avoid any public acknowledgment of religion's role in society."