As Tesla’s board of directors rallied Wednesday behind chief Elon Musk’s extraordinary push to take the all-electric automaker private, a growing contingent of investors, analysts and former regulators voiced doubts that the deal would ever take off.

Tesla’s board, a nine-member group that includes Musk’s younger brother, Kimbal, issued a belated statement Wednesday morning saying Musk had “opened a discussion” last week with the board about the benefits of taking Tesla private. The board, it said, had met “several times” over the past week and was actively working to “evaluate” the proposal.

But the board offered no further details of the proposal or its funding, sparking new questions about the feasibility of the surprise gambit Musk revealed in midday tweets Tuesday. “This is out there, even for Tesla,” analysts with Barclays wrote Wednesday.

The Securities and Exchange Commission also appeared interested in scrutinizing how the proposal first came to light. The SEC has asked Tesla for more information about Musk’s tweet, including proof that he had secured funding for the proposed buyout, according to a person briefed on the inquiry. The inquiry originated from the agency’s San Francisco office and doesn’t necessarily mean that the SEC will launch a formal investigation, the person said.

Musk could be at peril if the SEC finds that he made misleading public statements.

The inquiry was first reported by The Wall Street Journal. The SEC declined to comment, and the company and Musk did not immediately respond to requests for comment.

In a note to clients, Morgan Stanley analyst Adam Jonas said Musk’s strategy to reveal the offer on Twitter might end up leading to higher costs and financial risk. “Why announce it to the world in this way ... which could significantly contribute to the required premium and leverage?” Jonas asked.

Investors also seemed to be hesitant about the deal. Shares rocketed up 11 percent after Musk’s grand reveal Tuesday, with some expecting they would hit $420 — the price Musk promised shareholders would receive once the company had finalized its go-private transformation. But Tesla’s stock on Wednesday closed down more than 2 percent, at $370.

Cowen analyst Jeffrey Osborne told clients in a note Wednesday that he didn’t believe Tesla’s current business would “support a valuation anywhere close to $420 per share.”

Musk has played down the power of the tweets he launches at all hours to his 22 million Twitter followers: “My tweets are literally what I’m thinking at the moment, not carefully crafted corporate bs, which is really just banal propaganda,” he tweeted in June.

But his nine-word tweet during the middle of trading Tuesday — “Am considering taking Tesla private at $420. Funding secured.” — created what some lawyers are calling a potential battleground for lawsuits, regulator investigations and shareholder action.

Harvey Pitt, a former chair of the SEC, said Musk’s asserting a final sale price and that funding was “secured” opened him to potential charges of stock manipulation or securities fraud. “He has done enough things that might warrant somebody taking a close look,” Pitt said.

Neither Musk nor the board has said where the “secured” funding would come from. Tesla is a legendary cash-burner, with roughly $10 billion in debt and $2 billion in reserves, and Musk would probably need tens of billions of dollars to buy out shareholders at the right price.

The oil-rich kingdom of Saudi Arabia’s investment fund has gobbled up a multibillion-dollar stake in the company in recent months, the Financial Times reported Tuesday, but Tesla has not answered questions about the involvement of the kingdom, or anyone else, in how he would finance the company’s exit from public markets. The company offered no further detail beyond pointing to an all-employee email sent Tuesday by Musk.

It is also unclear how Musk came up with the $420 price. Company share prices, particularly in deals as giant as this one, are almost always decided by corporate executives, board members or consultants who review market data and optimize for maximum value.

“Just because” Musk wants it at $420 “doesn’t mean that there aren’t other people who might be willing to come in with another transaction that would be more beneficial to shareholders,” Pitt said. “This is very haphazard and raises, in my view, serious questions about why he would choose to do things in exactly this way.”

Lawyers said every word of Musk’s tweets will be examined, including why he used words such as “considering,” to determine whether he might have tried to inflate the stock price to blow out short-selling investors, a longtime Musk foe.

Investors have also questioned why the maneuver was not listed in a 69-page SEC filing, submitted last week and released Monday, that provided intricate details of Tesla’s financial outlook and coming events.

Teresa Goody, a former SEC official, said Musk “did something inappropriate and caused chaos in the market” in a way that would probably draw scrutiny from investigators. “Your disclosures should create certainty in the market so that everyone has a fair and complete understanding of what is going on,” Goody said.

Renae Merle contributed from New York.