Elon Musk has said that if Twitter could provide its method of sampling 100 accounts and how it confirmed these accounts are real, his $44 billion deal to buy the company should proceed on its original terms.
"However, if it turns out that their SEC [US Securities and Exchange Commission] filings are materially false, then it should not," Mr Musk tweeted.
In response to a Twitter user asking whether the SEC is probing "dubious claims" by the company, the Tesla CEO tweeted "Good question, why aren't they?".
Twitter declined to comment on the tweet when contacted by Reuters.
On Thursday Twitter dismissed Mr Musk's claim that he was hoodwinked into signing the deal to buy the social media company, saying that it was "implausible and contrary to fact".
"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.
"That story is as implausible and contrary to fact as it sounds," the filing released by Twitter said.
Mr Musk filed a countersuit Twitter on 29 July, escalating his legal fight against the social media company over his bid to walk away from the $44 billion purchase.
The Delaware Court of Chancery, where the dispute between the two sides is being litigated, has set a high bar for acquirers being allowed to abandon their deals.
Most legal experts have said the arguments in the case favour Twitter.
There is one scenario in which Mr Musk would be allowed to abandon the acquisition by paying Twitter only a $1 billion break-up fee, according to the terms of their contract
His $13 billion bank financing for the deal would have to collapse.
It is unclear whether the banks that agreed to finance the acquisition - Morgan Stanley, Bank of America Corp, Barclays Plc, Mitsubishi UFJ Financial GroupInc, BNP Paribas SA, Mizuho Financial Group Inc and Societe Generale SA - will attempt to get out of the deal.