WASHINGTON—Gary Gensler is facing a growing number of legal challenges as the Securities and Exchange Commission chair moves forward with wide-reaching efforts to squeeze Wall Street for the benefit of investors and companies.

A group of hedge funds sued the SEC on Tuesday in hopes of overturning a pair of recent rules requiring more disclosures around short selling and securities lending. The case was filed in the same conservative appeals court that looks set to kill another SEC rule aimed at getting investors more information about public companies’ share repurchases.