Mr. Musk’s feud with the S.E.C. stems from a Twitter post in August in which he claimed to have “funding secured” to take the company private at $420 a share. It was later revealed that he was referring to a much more embryonic proposal than he had implied. The S.E.C. sued Mr. Musk and Tesla, citing securities fraud.

In a settlement of that lawsuit, Mr. Musk agreed to step down as chairman and to get a lawyer to review written communications, including posts on Twitter, in which he made material statements about the company.

At a hearing two weeks ago on the S.E.C.’s request that Mr. Musk be held in contempt, Judge Alison J. Nathan of Federal District Court in Manhattan told the two sides to “take a deep breath” and put on “their reasonableness pants” to settle the matter, setting Thursday as the deadline.

In a submission approved by Judge Nathan on Thursday, the adversaries said that “while we have not reached an agreement,” they had conferred by phone for more than an hour this week “and are continuing to discuss potential resolution.” They said they would report back to the court by next Thursday “indicating whether we have reached an agreement in principle.”

The talks are going on as Tesla prepares for two important public presentations next week. On Monday, the company plans to outline its efforts to develop self-driving cars in a bid to convince Wall Street analysts that it has a competitive lead in that technology. On Wednesday, the carmaker will report its first-quarter results. Mr. Musk has said the company lost money in the quarter, after posting profits in the third and fourth quarters of 2018.