Mr. Musk’s involvement in politics and his financial support for the president’s campaign were 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.

Musk said he wants to form the America Party. A third party has never won the presidency, but they have influenced elections, experts say — mostly as spoilers.