SIOUX FALLS, S.D. — A Minnesota-based bank is asking a federal court to dismiss its lawsuit that sought to prevent debit card transaction fee limits from taking effect.

TCF National Bank, a subsidiary of TCF Financial Corp., sued Federal Reserve Chairman Ben Bernanke and its board of governors in U.S. District Court in South Dakota in October, saying the regulations were unconstitutional. The bank has said that the Durbin Amendment to the Wall Street Reform and Consumer Financial Protection Act of 2010 forces banks to do business below market rate and would mean a loss of $6 million a month for TCF National.

“While we continue to believe that the Durbin Amendment is unconstitutional because it requires below-cost pricing and exempts 99 percent of all U.S. banks, we believe our lawsuit has served its purpose in demonstrating the unfairness of the Durbin Amendment and that it is time for us to move on,” William Cooper, TCF National Bank’s chairman and chief executive, said in a statement Thursday. “The Federal Reserve Board’s final rule is an improvement from its initial proposal and recognizes many of the points we made in our case.”

Beginning this fall, banks will only be allowed to charge retailers 21 cents for each debit card transaction, plus an additional 0.05 percent of the purchase price to cover the cost of fraud protection. The Fed’s final rule issued Wednesday is not as punitive for banks as the Fed’s earlier proposal, which had sought to cap fees at 12 cents per transaction.

U.S. District Judge Lawrence Piersol had denied TCF National’s request for a preliminary injunction against the Fed, and an appeals court upheld that decision Wednesday. In its written ruling, the three-judge panel of the 8th U.S. Circuit Court of Appeals said that since TCF is free under the Durbin Amendment to assess fees on its customers to offset any losses, it’s skeptical that the amendment has created a price control on the bank’s debit-card business.

In 2009, $1.21 trillion in purchases were paid for with debit cards processed through the Visa and MasterCard networks, generating $19.7 billion in fees paid by merchants, according to data from The Nilson Report, a trade publication. Most of the fees went to banks that issue debit cards.

The Durbin Amendment exempts banks and credit unions with total consolidated assets under $10 billion. That, TCF National’s attorneys argued, gives thousands of unaffected banks an unfair advantage.

The U.S. Senate earlier this month voted to let the Federal Reserve limit the fees. Senators who wanted to block the Fed’s plan needed 60 votes to prevail, but the vote was six short at 54-45.