WASHINGTON—Elon Musk remains committed to settling fraud charges with the Securities and Exchange Commission, according to a legal filing Thursday, despite recently mocking the case against him.

Musk’s lawyers and the SEC submitted a joint legal filing Thursday that argues why a federal judge should approve separate settlements with the executive and Tesla Inc. TSLA, -1.26% which requires them to pay $20 million each in fines over statements he made on Twitter that regulators said were misleading. U.S. District Judge Alison J. Nathan had asked the two sides to explain why the deal should be approved.

The deal also calls for Musk to step down as Tesla’s chairman and for the company to add two new independent directors.

Musk risked reigniting his battle with securities regulators last Thursday when he appeared to ridicule the SEC, suggesting  it was enriching investors betting against the electric-car maker. “Just want to [say] that the Shortseller Enrichment Commission is doing incredible work,” Mr. Musk tweeted on Oct. 4. “And the name change is so on point!”

The joint filing submitted to the federal court said the settlements with Musk and Tesla are “fair, reasonable, and will serve the interests of the public and investors.”

An expanded version of this report appears at WSJ.com

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