Shares skidded as word spread of a criminal investigation triggered by Musk's Twitter comments. Tesla shares ended the formal Nasdaq trading day down 3.35 percent to $284.96.

Tesla said it was confident the matter would be quickly resolved with the Justice Department.

"Last month, following Elon's announcement that he was considering taking the company private, Tesla received a voluntary request for documents from the DOJ and has been cooperative in responding to it," the California-based company said.

"We have not received a subpoena, a request for testimony, or any other formal process."

A lawsuit filed earlier this month accuses Musk of trying to "burn" short-sellers by falsely tweeting that funding had been secured to take the electric carmaker private.

Musk surprised markets on August 7 by announcing on Twitter he wanted to take Tesla private at $420 a share, causing the stock price to jump. Short-sellers bet on share prices dropping.

Normally such a major announcement -- taking a huge company private -- would be explained in detail beforehand to regulators.

Musk has since backed off talk of going private, saying the company will continue to be publicly traded.

US market regulators are also scrutinizing what happened.

A number of executives have left Tesla of late. The company said last week that finance executive Justin McAnear is leaving as Tesla strives to become profitable by the end of the year.

Word that McAnear was heading for the off-ramp followed chief accounting officer Dave Morton's departure after just a month on the job, citing the company's frenetic pace.

Morton's brief tenure with the company coincided with the aborted go-private push.

- Erratic behavior -

Musk has also been criticized for other unorthodox behavior, including appearing on a podcast smoking marijuana and giving a tell-all interview to The New York Times in which he admitted to feeling overwhelmed and unable to sleep over Tesla's ambitious electric car production targets.

On Monday, British caver Vernon Unsworth filed a defamation suit against Musk for calling him a "pedo guy" and a "child rapist" on Twitter in a bizarre spat over the cave rescue in Thailand of a boys' soccer team and their coach.

Despite the myriad controversies, Musk continues to have a strong following with many investors and Tesla's market capitalization remains well above that of Ford and only slightly behind that of General Motors.

The latest news on Tesla comes as it seeks to ramp up production of its Model 3, the mass-market vehicle seen as key to the automaker's future.

Tesla had struggled to overcome production bottlenecks in recent months for the Model 3, but now faces other logistical issues, according to Musk.

"Service & parts supply in general will be the top Tesla priority after we get through the insane car delivery logistics of the next few weeks," Musk tweeted.

Musk is also CEO of SpaceX, the private space exploration firm that announced Monday that Japanese billionaire and online fashion tycoon Yusaku Maezawa will be the first man to fly around the Moon on a monster SpaceX rocket.