WASHINGTON — Limits on the fees banks charge merchants who accept debit cards would not apply to government-issued cards, under a tentative House-Senate deal aimed at easing worries raised by state treasurers.

The agreement announced Monday softens a Senate provision in a broad financial regulation bill that requires the Federal Reserve to limit the amount banks collect from merchants for every debit card transaction.

The provision, approved by the Senate last month 64-33, aimed to save retailers billions of dollars in debit card fees. Merchants said the charges resulted in inflated costs to consumers.

Under the tentative deal, the limits would not cover debit cards issued by the federal or state governments, which use the cards for programs such as unemployment or child support payments. Several state treasurers argued that restricting fees paid by merchants could force banks to increase charges for the cards to states.

Merchants typically pay between 1 percent and 2 percent of a debit card transaction to banks and the credit card networks, mainly Visa and MasterCard. Most of the money goes to the banks.

The agreement requires the Federal Reserve to set limits on those fees, based on what it considers “reasonable and proportional” to the cost to banks. The agreement allows the Fed, in determining the fee amount, to consider the banks’ costs of protecting against debit card fraud. The changes also would require the Fed to regulate only the fees set by banks, not by the credit card networks. The bulk of the fees are imposed by banks.

“Despite some improvements, this provision remains a terrible deal for consumers, for lower-income bank customers, for government benefits programs, and for community banks,” said Edward Yingling, president and CEO of the American Bankers Association. “The harm is real consumers will see higher costs, basic banking accounts in low-income communities will either be eliminated or involve higher prices, and government programs will cost taxpayers more money, all for the purpose of increasing merchant profits.”