The stock of the company was halted after it was reported that Musk would proceed with his deal to buy the company.
Musk offered to buy the company for $53.50 per share. The shares went up to $47.90 before the trading ended.
According to people familiar with the case who were not identified, Musk made the proposal in a letter to the micro-messaging service.
After agreeing to buy the social media platform in April, Musk has been trying to back out. The sale has been approved by shareholders. When Musk announced the deal was off, he claimed that the number of fake accounts on the platform was overstated.
Lawyers for Musk did not reply to messages on Tuesday.
Delaware Chancery Court is where the trial will be held in October.
Musk's argument for walking away from the deal was based on the allegation thatTwitter misrepresented how it measures the magnitude of "spam bot" accounts that are useless to advertisers The head judge of the court believed that something had changed since the April merger agreement was signed.