“Twitter’s own disclosures to the Musk parties show that although Twitter touts having 238 million ‘monetizable daily active users,’ those users who actually see ads (and thus, would reasonably be considered ‘monetizable’) is about 65 million lower than what Twitter represents,” Mr. Musk said in a court filing. The counterclaims were filed confidentially last week and unsealed Thursday in a late filing in Delaware Chancery Court.

Twitter board chairman Bret Taylor said in a tweet Thursday that Mr. Musk’s claims “are factually inaccurate, legally insufficient, and commercially irrelevant.” He linked to Twitter’s 127-page response and said the company looks forward to the trial in Delaware, which is scheduled for Oct. 17.

Twitter said in the response that Mr. Musk’s claim that he was misled is implausible and that the billionaire doesn’t have the right to back out based on his concerns over the number of spam or fake accounts on its platform.

“According to Musk, he—the billionaire founder of multiple companies, advised by Wall Street bankers and lawyers—was hoodwinked by Twitter into signing a $44 billion merger agreement,” Twitter wrote.

Twitter said that Mr. Musk hasn’t identified a false or misleading statement in Twitter’s disclosures.

“Musk invents representations Twitter never made and then tries to wield, selectively, the extensive confidential data Twitter provided him to conjure a breach of those purported representations,” Twitter said.

Mr. Musk has criticized Twitter’s reliance on ads, which account for about 90% of its revenue. He has said Twitter should shift toward a business model that relies more on subscriptions.

In his counterclaims, Mr. Musk said many users who are counted as monetizable don’t add to the company’s financial success, as Twitter represents, because most of the growth in monetizable daily average users see zero or almost zero ads.

“In fact, the majority of ads are served to less than 16 million users—a mere fraction of the 238 million” that Twitter cites to the market, Mr. Musk said.

Twitter said in its response that Mr. Musk is attempting to distort data and use litigation to undermine Twitter’s business. The company said its disclosures regarding monetizable daily average users in regulatory filings are accurate.

The company has long estimated that less than 5% of its monetizable daily users represent fake accounts, though it has also said in regulatory filings that the actual number could be higher.

Mr. Musk’s own analysis, which uses a publicly available website, indicates that false or spam accounts constitute at least 10% of Twitter’s monetizable daily active users, according to the filing Thursday.

The company says that estimate isn’t reliable because it isn’t using the same data as Twitter or measuring the same thing. Twitter has said that its process can’t be replicated externally because it is based on multiple human reviews of thousands of accounts sampled at random over time.

Twitter called into question an online application Mr. Musk has used to estimate bot figures, the Indiana University botometer, adding that the application had found that Mr. Musk’s own Twitter account was likely a bot.

Some data scientists say coming up with a precise, objective and authoritative number of fake or spam accounts on Twitter, where millions of tweets are posted daily, is an impractical task. There is no universal definition of fake or spam accounts, they say, and highly sophisticated technology can make posts seem as though they were written by humans when they were made by bots for nefarious purposes.

Mr. Musk has said that Twitter didn’t provide the necessary data and information he needs to assess the prevalence of such accounts and raised questions about Twitter’s methods.

Twitter has said it provided Mr. Musk with the information he requested. In its response Thursday to Mr. Musk’s counterclaims, the company said that it made “massive flows of data” available to him and that it “spent significant time and resources to compile, and in many instances create, data collections and information” requested by Mr. Musk.

Twitter sued Mr. Musk on July 12 in Delaware Court of Chancery to try to force him to go through with his takeover bid after he said in a July 8 securities filing that he wanted out of the deal.

Some of the counterclaims by Mr. Musk center on the allegation that Twitter updated its number of monetizable daily active users shortly after agreeing to the deal.

Twitter acknowledged in Thursday’s filing that it didn’t notify Mr. Musk before the merger agreement was signed April 25 that it had overstated its user base for nearly three years through the end of 2021. Twitter updated the numbers—which reflected less than a 1% change—in its April 28 earnings report, citing an error in how it accounted for people linked to multiple accounts. But the company argued that the earnings report didn’t include any materially false statements or admissions.

Mr. Musk alleged that Twitter proceeded to stonewall his requests for more details on the bot calculation because it knew the bull market was coming to a close and would show it was on weak footing, a reference to the

Warren Buffett

quote about a receding tide revealing who is swimming naked. Twitter said Mr. Musk doesn’t have “a shred of evidence” to support that theory.

Twitter scheduled a shareholder vote on Musk’s takeover for Sept. 13, saying in a regulatory filing last week that it is committed to completing the merger and that its board had unanimously recommended that shareholders vote in favor of the deal.

Write to Cara Lombardo at cara.lombardo@wsj.com, Erin Mulvaney at erin.mulvaney@wsj.com and Sarah Needleman at Sarah.Needleman@wsj.com