On Tuesday he tweeted that he had secured funding to buy all Tesla shares and take the company private.
One lawsuit, filed by Tesla investor Kalman Isaacs, said Musk's tweets amounted to a "nuclear attack" on short-sellers, created to "completely decimate" them for not believing in Tesla's stock to date.
Short-sellers borrow shares they believe are overpriced, sell them, and then repurchase shares later at what they hope will be a lower price to make a profit.
The proposed class-action complaint filed by Kalman Isaacs in San Francisco federal court accused Tesla and Musk of trying to artificially manipulate the company's stock price.
The US Securities and Exchange Commission (SEC) regulator contacted Tesla to inquire whether Musk's statements were factual and why the disclosure was made on Twitter rather than in a regulatory filing, according to media reports.More news: Trump condemns 'all racism' a year after Charlottesville
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"It is clear that Defendant Musk Tweeted materially false and misleading information regarding the Going Private Transaction to exact personal revenge and "squeeze-out" the short-sellers who had purportedly been badgering him for months", the complaint filed by Isaacs states.
Musk also said, with characteristic Kanye West arrogance, that the Tesla stock is "the most shorted stock in the history of the stock market" and that, as it is publicly traded, "there are large numbers of people who have the incentive to attack the company".
Mr Isaacs said he had bought 3,000 Tesla shares on 8 August to cover his short position.
It had also caused Tesla securities buyers to pay inflated prices, he claimed.
Tesla CEO Elon Musk used Twitter late Friday to taunt investors who have bet against his company, even though his previous Twitter comments have spurred a government investigation and shareholder lawsuits.