A cross honouring America's war dead that was stolen from a federal park in the Mojave Desert has been mysteriously replaced or returned.

A maintenance worker spotted the cross on Sunrise Rock, the same place a 7-foot (2.13-meter) metal cross had stood for decades, said Linda Slater, spokeswoman for the Mojave National Preserve.

The cross apparently was put up during the night, but it was unclear whether it was the original or a replica, Slater said.