The move comes after Musk sold around $8.5 billion worth of shares in the electric carmaker in April as he was preparing to finance a deal with the social media giant.
Twitter has dismissed Elon Musk's claim that he was hoodwinked into signing the $44B deal to buy the social media company, saying that it was "implausible and contrary to fact".
The richest man in the world is asking the court to free him from the agreement and make Twitter pay him an amount in damages to be determined at trial.
Musk's counter-suit was submitted along with a legal defence against Twitter's claim that the billionaire is contractually bound to complete the deal he inked in April to buy Twitter.
Attorneys for Musk claimed that Twitter’s proposed case schedule is “an obvious attempt to squeeze defendants” after a Delaware Chancery Court judge agreed last week to hold an expedited trial in a lawsuit filed by Twitter.
Twitter reported disappointing results, a miss that the social network attributed to "headwinds" including the uncertainty related to Elon Musk's buyout bid.
The relationship between the world’s richest man and the microblogging site has been tumultuous from the start and now it’s a legal battle.
The lawyers argued that the core dispute over false and spam accounts is fundamental to Twitter's value, is extremely fact- and expert-intensive, and will require substantial time for discovery.
"Musk apparently believes that he is free to change his mind, trash the company, disrupt its operations, destroy stockholder value, and walk away," reads the social media lawsuit.
Twitter shares have dropped nearly six percent in premarket trading after the social media company announced plans to sue Elon Musk for walking away from his buyout deal.
Musk had threatened to halt the deal unless the company showed proof that spam and bot accounts were fewer than 5 percent of users who see advertising on the social media service.
The report of the twins' arrival brings Musk's total count of children to nine.
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