The 7-foot-high cross was stolen late Sunday or early Monday by thieves who cut the metal bolts that attached the symbol to a rock in the sprawling desert preserve, National Park Service spokeswoman Linda Slater said.
Authorities had no immediate motive for the theft but Slater said possible suspects range from scrap metal scavengers to people "with an interest in the case," Slater said.
The U.S. Justice Department was looking into the case, and a veterans group planned to offer a $25,000 reward to help catch the thieves.
"The American Legion expects whoever is responsible for this vile act to be brought to justice," said Clarence Hill, the group's national commander. "While the memorial has been attacked, the fight will continue to ensure that veterans memorials will remain sacrosanct."
The cross came under legal fire about a decade ago by a former park service employee on grounds that it violated the constitutional separation of church and state. A lengthy court fight ensued, culminating with a 5-4 that said the cross should remain.
The cross had been covered with plywood since the early 2000s while the courts decided whether it was legal, but vandals tore off the wooden cover over the weekend. Maintenance workers went out to the rock to replace the cover and discovered the cross was missing, Slater said.
The Veterans of Foreign Wars first placed a wooden cross on the rock in 1934 to honor the dead troops of World War I. The latest cross - made of metal - was put up in the late 1990s by the memorial's longtime caretakers, Henry and Wanda Sandoz.
Wanda Sandoz said the cross had been vandalized in the past, but such instances had become rarer since her husband bolted it to the desert rock more than a decade ago.
"I was really upset and I was crying, and I said: 'Well, we'll show them. We'll put up a bigger one and a better one," she said. "And Henry said: 'No we won't. We will put one up exactly like the veterans put up."'
The VFW promised that the memorial will be rebuilt at its remote rock 70 miles south of Las Vegas and 200 miles northeast of Los Angeles.
"This was a legal fight that a vandal just made personal to 50 million veterans, military personnel and their families," National Commander Thomas J. Tradewell said.
It was not immediately clear whether they would be permitted to erect a new cross or whether a new cross would fall under the Supreme Court ruling.
"We're waiting for news from the Department of Justice as to what we should do. The case is still in litigation," Slater said.
The cross has provoked a tremendous amount of debate over the years among civil libertarians, veterans and the courts.
Federal courts ruled that the cross was unconstitutional and rejected a congressional effort to solve the issue by transferring the property into private hands.
The high court last month sent the property issue back to a lower court again and, in the meantime, refused to order its removal. Six justices wrote separate opinions.
Justice Anthony Kennedy wrote that the cross shouldn't be seen merely as a religious symbol.
"Here one Latin cross in the desert evokes far more than religion. It evokes thousands of small crosses in foreign fields marking the graves of Americans who fell in battles, battles whose tragedies are compounded if the fallen are forgotten," he wrote.
In dissent, Justice John Paul Stevens agreed that soldiers who died in battle deserve a memorial to their service. But the government "cannot lawfully do so by continued endorsement of a starkly sectarian message," Stevens said.
Peter Eliasberg, managing attorney at the American Civil Liberties Union of Southern California, which filed the lawsuit on the ex-worker's behalf, said his organization objects to the cross but condemns its theft.
"We believe in the rule of law and we think the proper way to resolve to any controversy about the cross is through the courts," he said. "We absolutely reject the idea of anybody engaging in theft or vandalism."
Eliasberg said he hasn't thought about what to do if the cross is replaced, but noted that the group had not objected to leaving up the current cross while it was covered.
Henry and Wanda Sandoz live about 160 miles away now in Yucca Valley, but neighbors and family frequently update them about conditions. They learned about the theft from one of their former neighbors on Monday.
"He's wanting to go right now and put another one up," Wanda said of her husband. "It's not going to be an easy thing to do. He's 71 years old and he's rarin' to go, I'll tell you."