Federal Judge Alison Nathan set a hearing in the case for April 4.
SEC lawyers moved late last month to have Musk found in contempt of court because Twitter posts the CEO put out about production numbers weren't reviewed by corporate authorities.
Musk had previously agreed to have his tweets about Tesla reviewed as part of a settlement of a securities fraud case with the SEC in September. That deal, which included $20 million fines for Musk and Tesla, came after the CEO tweeted falsely that he had financing to take the electric vehicle maker private at $420 a share.
In a court filing earlier this month, the SEC called the billionaire's February behavior "stunning," given the settlement he agreed to last September.
Attorneys for Musk countered that "The SEC's position is wrong at virtually every level," in their own legal filings last week.
The consequences of contempt of court finding could be serious for Musk.
The possibilities include new fines on Musk, a court-appointed communications monitor at Tesla, or even a trial that could result in the outspoken entrepreneur from being barred from serving as an officer or director of any public company, former SEC commissioner Harvey Pitt told TheStreet in late February.
Tesla shares rose $7.35, or 2.8% to $267.77 during the regular session Tuesday. The stock edged higher in after-hours trading.
Will You Have Enough Money Retire?
Want to learn about retirement planning from some of the nation's top experts? Join TheStreet's Robert "Mr. Retirement" Powell live in New York on April 6 for our Retirement Strategies Symposium. For a limited time, tickets are available for $99 for this full-day event. Check out the agenda, learn about the speakers and sign up here.