Elon Musk, in a surprise move that adds another twist to a monthslong drama that has preoccupied the tech industry, Wall Street and Washington, proposed a deal with Twitter on Monday evening that could bring to an end an acrimonious legal fight between the billionaire and the social media company.

The arrangement would allow Mr. Musk to acquire Twitter at $54.20 per share, the price he agreed to pay for the company in April, two people familiar with the proposal who were not authorized to speak publicly said.

But it was not immediately clear whether Twitter planned to accept his offer, which could be seen as a negotiating tactic by Mr. Musk to halt Twitter’s litigation against him. Mr. Musk is scheduled to be deposed on Thursday and Friday in Austin, Texas, according to a legal filing. Twitter could ask for court supervision for the deal to ensure that Mr. Musk follows through with his offer.

The potential deal comes after months of disputes that have created existential challenges for Twitter, cratering its share price, demoralizing its employees and spooking the advertisers it relies on for revenue.

A deal at the original price would be a victory for Twitter, which struck an agreement with Mr. Musk to buy the company for $44 billion. Mr. Musk declared in July that he no longer intended to complete the acquisition because he believed Twitter’s service was overrun by spam. Twitter sued him soon after to force him to complete the deal.

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Shares in the social media company spiked more than 12 percent on the news, before a halt in trading.

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