WASHINGTON—The Securities and Exchange Commission pushed back Friday on Tesla Inc.’s allegation that regulators are harassing Chief Executive Officer Elon Musk over his compliance with a 2018 regulatory settlement.

That deal focused on claims that Mr. Musk misled investors with a tweet in 2018 about taking the electric-vehicle maker private. The judgment required Tesla to preclear some of Mr. Musk’s public statements, including tweets deemed material to shareholders.