During the conference call accompanying the results, Mr Musk said he expected the company to avoid going back to the markets for capital and to be "essentially self-funding on a go-forward basis".
The SEC did not immediately respond to a request for comment on Musk's tweet.
Musk said he wants to take the $64 billion company private because of the "large numbers of people who have the incentive to attack the company".
The billionaire Musk, who owns about 20 per cent of the company, said a transaction would not "substantially" alter his stake and that he expected to continue to lead the company if it occurred.
The company's stock price jumped from US$342.54 ($460.76) prior to the announcement to US$379.57 ($510.60) at the day's close, a rise of nearly 11 per cent, but still significantly short of the proposed buy back price.
His missive came minutes after the Financial Times reported that Saudi Arabia's Public Investment Fund had built an undisclosed stake of 3 per cent to 5 per cent this year, citing people with direct knowledge of the matter it didn't identify. It zoomed as high as $371 per share before trading was halted at $367 per share just after 2 pm EDT. He added: "I can't believe this is something to bluff or make fun of". In follow-up tweets, Musk said shareholders could either sell at $420 or hold their shares and go private, adding that he was super appreciative of Tesla shareholders and would ensure their prosperity in any scenario.
The news caused Tesla's share price to jump by $14.
Here's what I envision being private would mean for all shareholders, including all of our employees.
Shortly after that news, Musk tweeted again that current shareholders would have the option of selling their shares at $420 or holding them privately.
"I would like to structure this so that all shareholders have a choice", Musk wrote. But he says any deal would be structured so that shareholders could opt to remain investors or be bought out at $420 per share.
He shared more details in a series of Twitter replies, noting that should Tesla go private, he'd remain in his role as founder and CEO of Tesla.
The electric vehicle maker reported revenue of $4 billion in the second quarter of 2018, with $2.2 billion in cash in hand.
"This has nothing to do with accumulating control for myself", Musk said in the Tuesday email.
Despite the unfolding media "shitshow", Musk still seems to view privatization as an "enormous opportunity for us all". Either way, the future is very bright and we'll keep fighting to achieve our mission.