Twitter has accused Elon Musk, in a lawsuit, of abandoning his planned acquisition of the company because stock market turbulence made the deal more difficult for him. But firing back in a legal filing, Mr. Musk says it was Twitter that torpedoed the $44 billion acquisition.

Mr. Musk argues that Twitter concealed the true number of inauthentic accounts on its platform, accusing the company of fraud. Such accounts made up at least 10 percent of Twitter’s daily active users who see ads, Mr. Musk’s legal team asserted, reiterating worries that he expressed shortly after signing the deal in April. Twitter has maintained that the figure is less than 5 percent.

Twitter also hid the number of its users who see ads, lawyers for Mr. Musk said in the filing, which was made public on Thursday. During the first quarter of the year, 65 million of the company’s 229 million daily active users did not see ads, according to the filing.

Twitter said that Mr. Musk was trying “to distort data received from Twitter to sponsor wild conclusions” and that its figures were accurate.

Using Botometer, a tool designed by Indiana University to measure inauthentic accounts, analysts for Mr. Musk found higher numbers of inauthentic accounts than Twitter had disclosed, according to the filing. Their analysis was preliminary and will be expanded, the filing said.

The misrepresentations hid weaknesses in Twitter’s business model and tricked Mr. Musk into agreeing to buy Twitter at “an inflated price,” lawyers for the Tesla executive said.

“Twitter was miscounting the number of false and spam accounts on its platform, as part of its scheme to mislead investors about the company’s prospects,” lawyers for Mr. Musk wrote. “Twitter’s disclosures have slowly unraveled, with Twitter frantically closing the gates on information in a desperate bid to prevent the Musk parties from uncovering its fraud.”

The filing, made last Friday but kept confidential until Thursday, was Mr. Musk’s first extensive response in what is expected to be a prolonged legal battle between the social media company and one of the richest people in the world. A trial is set for October.

“His claims are factually inaccurate, legally insufficient and commercially irrelevant,” Bret Taylor, the chairman of Twitter’s board, said in a statement on Thursday. The company also responded to Mr. Musk’s claims in a legal filing.

The Botometer tool is unreliable, Twitter said in its filing. The company noted that the tool used different standards from Twitter’s internal calculations and had once deemed Mr. Musk’s Twitter account “highly likely to be a bot.”

Mr. Musk began snapping up shares of Twitter early this year and by April had become the company’s largest shareholder. He rejected Twitter’s offer to join its board, instead launching a swift and aggressive takeover attempt. But once Twitter agreed to the acquisition, Mr. Musk began to express doubts. In July, he indicated that he no longer wanted to buy the company.

Twitter sued Mr. Musk in Delaware Chancery Court in an attempt to force the acquisition through. Twitter has claimed he lost interest in the deal as the market slumped and shares in Twitter and the electric carmaker Tesla, which is the primary source of Mr. Musk’s wealth, declined.

“Musk refuses to honor his obligations to Twitter and its stockholders because the deal he signed no longer serves his personal interests,” Twitter said in its lawsuit.

Over the last few days, the company peppered Mr. Musk’s banks, financial partners and associates with subpoenas, demanding communications about the deal that could shed light on why Mr. Musk decided to walk away.

The deal includes a “specific performance” clause that allows Twitter to sue to force the deal through so long as the debt that the billionaire has corralled for the acquisition is in place. But Mr. Musk may pay a $1 billion fee to exit the deal if his funding falls through.

Mr. Musk has maintained that Twitter is flooded with fake accounts and that the company has misled him about the true number of impostors on its platform. Fake accounts are used to spread spam or manipulate Twitter’s service by falsely amplifying trends, and are often automated rather than run by real people.

Twitter earns the bulk of its revenue from advertising. But Mr. Musk asserted that advertisers would not reach the customers they intended if Twitter was flooded with fake accounts. His lawyers argued that inaccuracies in Twitter’s user metrics amounted to a material adverse affect on the business, allowing him to abandon the acquisition.

Twitter said in a message to employees that was seen by The New York Times that it had chosen not to redact any of Mr. Musk’s claims because it was confident in its metrics. “We offer our customers a highly sophisticated set of tools and features to run and measure the effectiveness of their campaigns across our platform, with a foundation of transparency,” said Sean Edgett, Twitter’s general counsel.

On Thursday, Mr. Musk continued to weigh in on how Twitter could change. “I do understand the product quite well, so I think I’ve got a good sense of where to point the engineering team at Twitter to make it radically better,” he said during a meeting of Tesla shareholders.

Mike Isaac and Jack Ewing contributed reporting.