Retailers are suing the Federal Reserve over new limits on controversial debit card swipe fees that the industry says are too high.

Swipe fees, also known as interchange, are paid by merchants to banks each time a shopper swipes a debit card. The Fed issued new rules that took effect last month capping that fee at 24 cents for a typical transaction of $38.

But in their appeal of the rule filed Tuesday in U.S. District Court, retail groups argue that the amount allows banks to recoup costs specifically excluded by law, such as fraud losses. Although the new limit is less than the historic average of 44 cents per transaction, it is still significantly higher than the Fed’s initial plan to cap the fees at 12 cents.

“It was very, very clear,” Mallory Duncan, general counsel for the National Retail Federation, one of the groups leading the suit, said of the law. “This is not a happy day.”

A Fed spokesman said it is aware of the lawsuit and will be reviewing it.

Swipe fees have become a flash point in what had long been an arcane and obscure battle between merchants and banks. Retailers won round one when they persuaded Sen. Richard J. Durbin (D-Ill.) to attach an amendment to the financial reform legislation passed last year that directed the Fed to limit the fees.

Banks fought back fiercely, narrowly losing an effort this summer to overturn the law. The industry considered the Fed’s move to a 22-cent cap an improvement but warned that many financial institutions would seek to recover lost revenue through higher fees to consumers. That’s what prompted Bank of America to announce in September that it would charge customers $5 a month to use their debit cards. The move quickly sparked consumer outrage, and the bank soon dropped the fee.

But the fight over swipe fees is far from over, especially because big money is at stake. In the retailers’ suit, department store chain Boscov’s said it pays banks between $7 million to $8 million annually in swipe fees. Miller Oil in Norfolk said in the suit that the Fed’s new rules mean that it will pay higher fees. The company said it paid banks a percentage of each purchase, about 16 cents for an average transaction of $3.72 at its convenience stores. Now it will pay at least 21 cents.

“Miller will suffer significant and irreparable monetary injury directly traceable to the [Fed’s] misconstruction of the Durbin amendment,” the suit says.

Still, Richard Hunt, president of the Consumer Bankers Association, a trade group, said retailers only have themselves to blame.

“They spent millions of dollars determining the game, setting the rules of the game and don’t like the results,” he said. “Sounds like sour grapes to me.”

The National Association of Convenience Stores and the Food Marketing Institute are also parties in the suit.