Mr Musk tweeted that the deal "cannot move forward" unless Twitter backs up its claims that less than 5% of daily users are fake or spam accounts.
Twitter has defended its figures, adding that Mr Musk waived rights to "due diligence" to clinch the deal.
The spat has raised doubts about the takeover.
Analysts have speculated that Mr Musk may be looking for ways to renegotiate the price of the deal or walk away.
Mr Musk agreed the $44bn (£34.5bn) deal to buy Twitter with its board in April, but last week Mr Musk said the deal was "on hold" while he sought details about fake accounts.