Tesla shares have dropped back to near the level they were trading at before CEO Elon Musk tweeted Tuesday that he may take the company private.

Shares were down 6 percent to $347.26 in midday trading Thursday.

Shares had closed at $341.99 on Monday. Then Musk's Tuesday morning tweet that he might take the company private at $420 a share sent them soaring to $379. 57.

The SEC already has opened an inquiry into the wording and method of Musk's disclosure about the deal, according to a Wednesday report in The Wall Street Journal, which cited unidentified people familiar with the matter.

Musk acknowledged he was serious in an email to employees, and Tesla directors have said they're evaluating it.