Federal securities regulators have served Tesla with a subpoena, according to a person familiar with the investigation, increasing pressure on the electric car company as it deals with the fallout from several recent actions by its chief executive, Elon Musk.

The subpoena, from the Securities and Exchange Commission, comes days after regulators began inquiring about an Aug. 7 Twitter post by Mr. Musk, in which he said he was considering converting Tesla to a private company. In the post, he said that the financing for such a transaction, which would probably run into the tens of billions of dollars, had been “secured.”

Tesla shares, a popular target for so-called short sellers who bet on certain stocks losing value, soared about 11 percent on the day Mr. Musk posted the message.

It has become clear since then that neither Mr. Musk nor Tesla had actually lined up the necessary financing aside from having preliminary conversations with some investors.