The directors Brad Buss, Robyn Denholm, Ira Ehrenpreis, Antonio Gracias, Linda Johnson Rice and James Murdoch said: "Last week, Elon opened a discussion with the board about taking the company private". The board, they said, had met "several times" over the last week and was actively working to "evaluate" the proposal.
Musk's tweets caused a flurry of activity in financial markets.More news: Oscars introduce new award for outstanding popular film
Tesla's shares were down 2.1 percent at $371.70 on Wednesday after closing up 11 percent on Tuesday.
In a later statement to employees and posted on Tesla's blog, Musk explained: "Being public. subjects us to the quarterly earnings cycle that puts enormous pressure on Tesla to make decisions that may be right for a given quarter, but not necessarily right for the long-term". If the statement regarding having secured the funding for the move later proves unachievable, then Musk could be in hot water with regulators over the statements that he first made on Twitter.
In subsequent tweets, Mr. Musk said that going private would end "negative propaganda" from short sellers.More news: Pink is resting-up after health scare in Sydney
Cowen analyst Jeffrey Osborne told clients in a note Wednesday that he didn't believe Tesla's current business "support a valuation anywhere close to $420 per share".
China's Tencent Holdings Ltd, which took a 5-percent stake in Tesla a year ago, could also be a possible partner. The move would also foreclose the option of selling more stock to raise cash every year, a move which Musk has disfavored in recent years.
A statement was issued by six members of the electric carmaker's board after Mr Musk tweeted to say he had the funding to de-list the company. The transaction would amount to the largest leveraged buyout - in which a company borrows money to repurchase shares and exit the public market - of all time. Company share prices, particularly in deals as giant as this one, are nearly always decided by corporate executives, board members or consultants who review market data and optimize for maximum value.More news: Snapchat drops daily users for first time after controversial redesign
Former SEC chair Harvey Pitt told CNBC that while the United States stock market regulator permits executives of publicly listed companies to use social media to make statements about their businesses, Musk's tweet was still "highly unprecedented".