Shares of electric car maker Tesla have tumbled about 9 per cent after CEO Elon Musk conceded in a newspaper interview that job stress may be getting the best of him.

Tesla shares closed at $US305.50 ($417.56) on Friday (local time), their lowest level since August 1, as analysts and business professors questioned whether the company's board should grant Mr Musk leave or even replace him with a more seasoned CEO.

The decline lopped $US5.4 billion off Tesla's market value.

In an interview with the New York Times Mr Musk admitted the past year had been the most "difficult and painful" of his career.

The newspaper reported that during an hour-long telephone interview Mr Musk alternated between laughter and tears, acknowledging he was working up to 120 hours a week and sometimes took Ambien to get to sleep.

"It's kind of bizarre," said Charles Elson, director of the corporate governance centre at the University of Delaware.

"It's a drama we shouldn't be watching."

Still, Mr Musk said in the interview he had no plans to give up his dual role as Tesla's chairman and CEO.

"If you have anyone who can do a better job, please let me know. They can have the job. Is there someone who can do the job better? They can have the reins right now," he said.

Board supports Musk

Since the interview Tesla's board had shown no sign of taking any action. In a statement, the directors — excluding Mr Musk himself — praised the CEO's dedication to the company.

"Over the past 15 years, Elon's leadership of the Tesla team has caused Tesla to grow from a small start-up to having hundreds of thousands of cars on the road that customers love, employing tens of thousands of people around the world, and creating significant shareholder value in the process," the statement said, without addressing Mr Musk's recent behaviour.

Elon Musk admitted he wrote one of his controversial tweets inside a Tesla Model S while driving to the airport. ( Reuters: Kim Hong-Ji )

The interview puts board members in a difficult position because Mr Musk, who entered Tesla as a major investor and built the company into a force that has changed the perception of electric cars, is the company's public identity.

But Erik Gordon, a University of Michigan business and law professor, said Tesla's board had a fiduciary duty to shareholders to take action.

"If the board does not get him out of this slot, at a minimum on a leave-of-absence basis, I think the board is going to be seen by a lot of people who love the company as being derelict in their duties," Professor Gordon said.

"You can love the company, you can love Musk and hate having him be the CEO at this point."

The board has stood behind Mr Musk despite some bizarre behaviour. In July he labelled a diver who aided in the cave rescue of Thai soccer players as a paedophile. He later apologised.

But a tweet Mr Musk fired off last week reportedly made him and the directors the targets of securities regulators, and may force the board to act.

Mr Musk tweeted he had "funding secured" to take Tesla private and avoid the quarterly earnings pressures from Wall Street. The out-of-the-blue announcement raised a huge ruckus and pushed Tesla's shares up 11 per cent in a day, boosting the company's value by $US6 billion.

There were multiple reports the US Securities and Exchange Commission was investigating the disclosure, including asking board members what they knew about Mr Musk's plans. Experts said regulators were likely investigating if Mr Musk was truthful in the tweet about having the financing set for the deal.

In New York Times interview, Mr Musk stood by the tweet. But he told the newspaper he wrote the tweet inside a Tesla Model S while he was driving to the airport, and that no-one else reviewed it.

Asked if he regretted it, he said: "Why would I?"

In a separate report, The Wall Street Journal said securities regulators had been investigating if Tesla misled investors about Model 3 production problems.

The company could face sanctions if regulators find it did not accurately portray production delays to investors.

Questions over Musk's future as CEO

The New York Times cited people familiar with the situation as saying the board had been trying to find a No. 2 executive to help relieve some of the pressure on Mr Musk.

Mr Gordon said the board had to act now or be open to shareholder lawsuits. He suggested replacing Mr Musk as CEO and keeping him on as a visionary chief technical officer.

The interview and other actions, Mr Gordon said, were signs Mr Musk could no longer handle the CEO job.

Mr Musk spent nights at Tesla's Fremont, California, factory working out production problems on its new Model 3 car that is supposed to take Tesla from niche luxury carmaker to a mass producer that competes with Detroit.

But Mr Gordon said a CEO would not live at the factory. Instead, he or she would form a team to work overnight and solve problems.

The company said the board formed a special committee to evaluate proposals to take the company private. It later disclosed that Mr Musk had talked with the Saudi Arabia Government investment fund about the deal.

Some of Mr Musk's stress comes from critical short-sellers who are betting against the company's success. But much of it comes from Mr Musk's own pronouncements, such as lofty goals for production of cars or turning a sustained profit starting this quarter, that might be beyond reach.

Tesla has never made money for a full year and has had only two profitable quarters since it went public in 2010.

AP/ABC