SAN FRANCISCO — On Friday night, more than two dozen Native Americans embarked from here on a spiritual mission to New Zealand, where they will ask their fish to come home to California.

The unusual journey centers on an apology, to be relayed to the fish on the banks of the Rakaia River through a ceremonial dance that tribal leaders say has not been performed in more than 60 years.

The fish in question is the Chinook salmon, native to the Pacific but lately in short supply in the rivers of Northern California, home to the Winnemem Wintu — a tiny, federally unrecognized and poor tribe supported by some Social Security payments, a couple of retirement plans and the occasional dog sale.

As the Winnemem see it, the tribe’s troubles began in early 1940s, with the completion of the Shasta Dam, which blocked the Sacramento River and cut off the lower McCloud River, obstructing seasonal salmon runs, and according to the tribe, breaking a covenant with the fish.