WASHINGTON—The Federal Reserve proposed on Wednesday easing a rule designed to curb risky trading in the wake of the financial crisis, one of the most significant deregulatory measures for banks since President Donald Trump took office.

The proposal, unanimously advanced by the Federal Reserve and known as Volcker 2.0, means JPMorgan Chase & Co., Goldman Sachs Group Inc. and other banking behemoths would face fewer audits of individual securities and derivatives transactions. The banks wouldn’t have to spend as much time proving...