The chief executive of electric car maker Tesla Inc has filed a $44 billion takeover bid for the social media platform, Reuters reports.
Investors said Musk had saved himself $156 million by failing to disclose that by 14 March he had acquired more than 5 percent of Twitter stock.
They also named Twitter as a defendant, arguing the company had an obligation to investigate Musk's conduct, though they are not seeking damages from the firm.
Investors said Musk continued to buy stock after that and eventually disclosed in early April that he owned 9.2 percent of the company.
"By delaying his disclosure of his stake in Twitter, Musk engaged in market manipulation and bought Twitter stock at an artificially low price," said the investors, led by Virginia resident William Heresniak.
The investors said the recent drop in Tesla's stock has put Musk's ability to finance his acquisition of Twitter in "major peril" since he has pledged his shares as collateral to secure the loans he needs to buy the company.
The timing of Musk's disclosure of his stake has already prompted an investigation by the U.S. Securities and Exchange Commission (SEC), the Wall Street Journal reported.
The SEC requires any investor who buys more than a 5 percent stake in a company to disclose its assets within 10 days of crossing the threshold.
The investors also said public criticism by Musk of the company, including a May 13 tweet stating the buyout was "temporarily on hold" until Twitter proved that spambots accounted for less than 5% of its users, amounted to an attempt to further drive the share price down.
