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.

MSNBC host Jen Psaki breaks down the barriers Elon Musk will face in creating a third political party, and why he'll likely fail

Tesla CEO Elon Musk's plan for a new political party prompted an analyst to recommend Tesla's board board create new "ground rules" to keep Musk focused on Tesla's future.

The two men spoke about Mr. Musk’s push to create the America Party before the midterm elections. Mr. Yarvin has expressed support for a monarchy, along with provocative ideas about race.