WASHINGTON—The Federal Reserve proposed lowering by about 30% the fees merchants pay to many banks when consumers shop with debit cards, setting off a fight with banks that oppose the changes. 

At present, merchants pay large card issuers such as JPMorgan Chase and Bank of America 21 cents plus 0.05% of the transaction amount, which is the level set by the Fed in 2011. The Fed can lower the cap if it determines the costs for processing debit-card payments are declining, but it had never previously done so.