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More than 10 years ago, Arnold Schwarzenegger, then the Republican governor of California, told an audience of conservative leaders that the California Republican Party had moved too far to the right and was “dying at the box office.”

“How right I was,” Mr. Schwarzenegger said in a rare return public appearance on Wednesday. “The party was going down and down and down. Today we are the Titanic after it hit the iceberg — but before the last bit of the ship submerged.”

Mr. Schwarzenegger was speaking at a youth center in East Los Angeles marking the start of an organization of moderate California Republicans trying to move the way-out-of-power state party to the center — and back, organizers said, into being a player in state governance. The organization is called New Way California and was put together by Assemblyman Chad Mayes, who was ousted as the Republican minority leader after voting with Democrats on extending the cap-and-trade automobile emission program.

“We seek to shed the stereotype of the intolerant Republican Party that serves only the rich and big business,” Mr. Mayes said.