Mr. Musk’s involvement in politics and his financial support for the president’s campaign was once seen by investors as a benefit to Tesla, fueling a steep rise in company shares after the election last year. That association has now turned into a liability. Tesla shares are down 40 percent from their peak in December.

Elon Musk says he has formed a new political party called the America Party. But it remains unclear what formal steps, if any, he has taken to establish it.