The three custody banks — Bank of New York Mellon, State Street and Northern Trust — would, when calculating how much capital to hold on their balance sheets, be able to set aside deposits they received from other banks and immediately gave to the Federal Reserve or another central bank for safekeeping.

Jennifer Hendricks Sullivan, a spokeswoman for Bank of New York Mellon, said in an email that the exemption was structured in a way that “recognizes the unique business model of the custody banks.”

Citigroup and JPMorgan argue that the exemption is not fair. They say that since they, too, take deposits from other banks and stash them at the Fed, they should get the same relief — even though that is not the primary focus of their business. Lobbyists for the two banks are hoping to persuade lawmakers to change the bill to allow all banks that accept custodial deposits to take advantage of the exemption, according to people familiar with the banks’ efforts who spoke on condition of anonymity because they were not authorized to discuss those efforts.

“As Congress has sought to make a common sense change to the way capital rules treat custody assets, we have asked that they apply that change to all custody banks to maintain a level playing field in this important business,” a Citigroup spokesman said in an email on Friday.

Spokesmen from JPMorgan and State Street declined to comment.

Whether the language is broadened or not, the presence of a carve-out has made supporters of the law’s original capital requirement nervous. They say its purpose is to keep banks from convincing regulators that certain products aren’t dangerous when they may ultimately pose a risk.

“This is not a tweak,” said Sheila C. Bair, former chairwoman of the Federal Deposit Insurance Corporation. “This could be a very significant weakening of bank capital rules.”