Twitter shares are up after it filed a lawsuit against Elon Musk.

Twitter shares jumped Wednesday after a hedge fund revealed it had taken a stake in the firm based on its "strong case" against Elon Musk for moving to back out of his $44 billion buyout bid.

Stocks in the social media platform, which sued Tuesday to force the mercurial billionaire to stick to the deal, were up around eight percent in trading.

The hedge fund, Hindenburg Research, took a "significant" stake in Twitter, but one which is below the five percent line that requires reporting to US market watchdog Securities and Exchange Commission, the fund's founder Nathan Anderson confirmed to AFP.

Anderson said it was the first time that Hindenburg had publicly revealed the purchase of shares.

"Twitter is suing to enforce the entire $44 billion merger price and they have a strong case," Anderson said.

The suit filed in the US state of Delaware urges the court to order the Tesla boss to complete his deal to buy Twitter, arguing that no financial penalty could repair the damage he has caused.

After weeks of threats, Musk last week pulled the plug on the deal, accusing Twitter of "misleading" statements about the number of fake accounts, according to a letter from his lawyers included in a US securities filing.

"Twitter's bot issue is perhaps the worst pretext Musk could have chosen for terminating the deal given that it was clearly and publicly a reason he entered the agreement in the first place," Anderson added.

A few days after he made an offer in April to buy the company, Musk said that if the acquisition was finalized, he would "defeat the spam bots or die trying!"

For Anderson, Twitter has "more leverage" given the potential threat to Musk's empire in the event of an outright win in court.

Wedbush Securities analyst Dan Ives said in a note that Wall Street is "interpreting the Twitter suit against Musk filed last night as 'extremely compelling.'"

"The stock is now factoring in some significant chance that Musk will ultimately have to pay Twitter a settlement well north of $1 billion," said Ives, referring to the breakup fee in the original agreement between the entrepreneur and Twitter.