NEW YORK – The Federal Reserve on Thursday proposed a 12-cent cap on the fees banks would be allowed to charge merchants for debit card transactions, a limit that could sharply cut into the revenue of the banks that issue debit cards.

Capping debit interchange fees, or “swipe” fees, would help merchants by replacing the current system, in which they generally pay between 1 percent and 2 percent of the dollar value of each transaction.

Bank stocks were largely unaffected by the news, but shares of Visa and MasterCard both fell sharply following the announcement.

Fed staff members said consumers would not likely see a swipe fee cap translate into lower prices, except in some highly competitive markets.

It may, however, result in banks cutting back on debit card reward programs or searching for other ways to offset the loss of income that would be caused by lower fees.

The proposal is being made to enact a provision of the financial regulatory overhaul bill that became law in July.

The provision requires that interchange fees be “reasonable and proportional” to banks’ costs for processing transactions.

The National Retail Federation was among merchant groups that praised the proposal, saying fee limits “would result in lower costs for merchants and could lead to discounts for their customers.”

The American Bankers Association had a vastly different take, charging that the cap would “essentially relieve retailers of paying their fair share for a card payments system that offers them tremendous benefits.”

Visa shares plunged $9.75, or 12.7 percent, to $67.19.

MasterCard shares plunged $25.73, or 10.3 percent, to $223.49.