Mr. Musk’s lawyers asked on Friday for a trial date on or after Feb. 13 of next year, saying they need more time to drill down into the fake and spam account issue that the billionaire has cited as the chief reason for terminating the deal. They added the debt financing was valid until April 25, 2023.

A remote hearing is scheduled for Tuesday morning on Twitter’s motion to expedite the case.

Twitter said in the filing Monday that Mr. Musk’s alleged core issue—an accurate count of fake and spam accounts—is a “contractually irrelevant sideshow.”

Last week Twitter sued Mr. Musk in Delaware Chancery Court, seeking to force Mr. Musk to honor the terms of the deal after he moved to abandon it. The company asked the court to expedite the proceedings, citing risks from the recent economic downturn and being held in limbo by a buyer.

Mr. Musk has said he wants out of the deal because Twitter didn’t provide him with the necessary data and information he needed to assess the prevalence of fake or spam accounts on its platform. The company has long estimated that less than 5% of its monetizable daily active users fit that description, while Mr. Musk has said it is likely closer to 20%.

On Friday, Mr. Musk’s lawyers filed a motion to oppose an expedited trial, arguing that the dispute over false and spam accounts “is fundamental to Twitter’s value” and “extremely fact and expert intensive, requiring substantial time for discovery.” The document was the first in which Mr. Musk’s side laid out publicly a clear timeline around his concerns over data about fake and spam accounts and included new claims about Twitter’s level of cooperation on the issue.

In its response Monday to Mr. Musk’s motion, Twitter said the billionaire hasn’t offered a sound reason for delaying the trial and it noted that the Delaware Chancery Court has previously resolved many merger-enforcement disputes within 60 to 75 days, which is in line with the schedule it is seeking for its case against Mr. Musk.

Twitter added that getting the trial under way quickly is “imperative” because the dispute itself is harming its business and that Mr. Musk is amplifying the problem by using the platform to disparage the company. Employees, customers and shareholders have been hurt as a result, the company said.

“No public company of this size and scale has ever had to bear these uncertainties,” Twitter said.

Twitter said in its suit against Mr. Musk that it thinks the real reason he is looking to exit from the deal is that market conditions have soured since he made his bid for it, resulting in his personal wealth declining by more than $100 billion from its November 2021 peak. The company also said it had bent over backward to accommodate the billionaire’s data requests, including by giving him access to its so-called fire hose of near real-time tweets as well as historical tweets.

Mr. Musk’s side has alleged in court filings that the

Tesla Inc.

CEO’s interactions with Twitter were akin to “a two-month treasure hunt of delays, technical bottlenecks, evasive answers, and, ultimately, refusals.” His team said they became concerned about Twitter’s user numbers after the company announced revisions in its first-quarter earnings in April. Twitter said then it had overstated its user base for nearly three years through the end of 2021 because of an error in how it accounted for people linked to multiple accounts. The revision reduced the number of monetizable daily active users by 0.9% for the fourth quarter of last year.

In a May 6 meeting with Twitter executives about how spam is calculated, Mr. Musk ’s team on Friday said he was “flabbergasted to learn just how meager Twitter’s process was” and pointed to the absence of automated tools to help with the calculation.

Write to Sarah E. Needleman at sarah.needleman@wsj.com and Cara Lombardo at cara.lombardo@wsj.com