Trading in shares of Twitter was halted after the stock spiked on reports that Elon Musk would proceed with his $44 billion deal to buy the company after months of legal battles.

For a second time, Mr. Musk offered to buy the San Francisco company at $54.20. Shares jumped nearly 13 percent to $47.95 before trading stopped.

Bloomberg News reported Tuesday that Mr. Musk made the proposal in a letter to Twitter, according to people familiar with the case who were not identified.

Mr. Musk has been trying to back out of the deal for several months after signing on to buy the social media platform in April. Shareholders have already approved the sale. Mr. Musk claimed that Twitter under-counted the number of fake accounts on its platform, and Twitter sued when Mr. Musk announced the deal was off.

Neither Twitter nor lawyers for Musk responded to messages seeking comment on Tuesday.

The trial seeking to compel Mr. Musk to buy Twitter is set to start at Delaware Chancery Court on October 17.

Mr. Musk’s argument for walking away from the deal has largely rested on the allegation that Twitter misrepresented how it measures the magnitude of “spam bot” accounts that are useless to advertisers. 

Yet most legal experts believed he faced an uphill battle in convincing the court’s head judge, Chancellor Kathaleen St. Jude McCormick, that something changed since the April merger agreement that justifies terminating the deal.

Legal experts generally have said that Twitter had the upper hand in the lawsuit, which Twitter filed in July. Twitter is seeking “specific performance” of the contract with Mr. Musk, which means he would have to go through with the purchase at the original price. The contract Mr. Musk signed also has a $1 billion breakup fee.

“This is a clear sign that Musk recognized heading into Delaware Court that the chances of winning vs. Twitter board was highly unlikely,” Wedbush analyst Dan Ives wrote in a note to investors. 

He added: “Being forced to do the deal after a long and ugly court battle in Delaware was not an ideal scenario, and instead accepting this path and moving forward with the deal will save a massive legal headache.”

Among the remedies that would favor Twitter is a court order to go through with the deal. The Chancery Court last year forced private equity firm Kohlberg & Co. to go through with its $550 million buyout of DecoPac, a company based in Minnesota that calls itself the world’s largest supplier of cake decorating supplies to professional decorators and bakeries. 

The case was emblematic of the court’s common — though not uniform — resolution of enforcing contractual obligations on buyers.

Other options include Mr. Musk being forced to pay the breakup fee each side agreed to if deemed responsible for the deal falling through. Or he might have to pay off a larger amount without actually buying the company for $44 billion.

Legal experts have said that Delaware courts have been picky about interpreting what counts as a valid reason for backing off of a deal. The gap between what Mr. Musk knew about Twitter when he made the offer in April and the state of the company today had to be huge, and there’s little evidence of that, one lawyer said.