WASHINGTON — Retailers won a big victory last summer when the Federal Reserve cut by half the fees that banks and credit card companies were charging them to process debit card transactions.

For some retailers, however, that was not enough. This week, trade groups representing retailers, convenience stores and grocers filed a lawsuit against the Fed, asserting that the board’s debit fee rules — which allow an additional variable fee to cover fraud costs — violate the law passed by Congress as part of the Dodd-Frank financial regulation package. The lawsuit was filed in United States District Court in Washington.

The rule, which went into effect in October, was the subject of fierce lobbying by banks and retailers over what has grown to $20 billion in annual debit card transaction fees. Consumers do not pay the fees directly but merchants have complained that rising fees in recent years have forced them to raise prices.

In a sort of Solomonic decision, the Fed approved a cap of 21 to 24 cents a transaction, down from an average of 44 cents that had been being charged. But the new fee cap was roughly double the 12 cents initially proposed by the Fed before banks and credit card companies pushed to raise it.

Mallory Duncan, senior vice president and general counsel for the National Retail Federation, said in an interview that the main problem with the Fed’s new fee structure was that it allowed banks and card companies to add a variable charge of up to 5 basis points — or five one-hundredths of a percentage point — to each transaction in order to recover a portion of fraud losses.

“The law specifically said that they could recover fraud prevention costs,” but it does not allow for the recouping of actual losses, Mr. Duncan said.

Banks also can include in their fees the cost of updates to their processing equipment, he said. That benefits the overall operations of banks and card companies, but does not directly relate to specific debit card transactions, as the law requires, he said.

“The Fed did a very credible job of investigating what the incremental costs of debit card transactions were,” Mr. Duncan said. “But the Fed didn’t follow the law, so everyone’s fees are higher than they should be.”

A spokeswoman for the Federal Reserve said the board was aware of the lawsuit and “will be reviewing it,” but she declined further comment.

Mr. Duncan said the Fed’s rule had particularly harmed merchants that handle mostly small-ticket purchases — fast-food outlets, convenience stores and the like.

Before the new rules were created, those companies typically paid a fee of 11 to 12 cents on a $5 purchase, Mr. Duncan said. Now, banks have adopted the Fed’s fee structure as a minimum charge on all transactions, meaning that fees on small-ticket items have doubled.

Trish Wexler, a spokeswoman for the Electronic Payments Coalition, which represents card companies, banks and other issuers of debit cards, said the lawsuit by retailers was “a matter of greed.”

“Retailers won’t be truly happy until they pay zero to accept cards,” Ms. Wexler said. “They don’t want to pay anything for this system, which produces for them more revenues, more customers and more security.”

Mr. Duncan said the lawsuit was not motivated by greed. “The nature of our business is extremely competitive,” he said. “Our profit margins are probably the narrowest of any industry in America.”

After the new debit fee rules went into effect, some banks, Bank of America most prominent among them, said they would begin to charge customers a monthly fee of about $5 to use debit cards. After an uproar by consumers, the banks backed off the proposal.

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