Twitter's stock price rose 27 percent once Musk belatedly disclosed his stake, the lawsuit said. "During the period that Musk was required to publicly disclose his beneficial ownership but had failed to do so, he spent more than $500 million purchasing additional shares of Twitter common stock," it said.

The lawsuit marks the latest salvo in a years-old feud between the SEC and Musk, who has become one of the regulator's highest-profile critics.