Top executives from six major U.S. banks on Wednesday discussed concerns over new industry regulations and the central bank's recent "stress tests" with Federal Reserve Gov. Daniel Tarullo, the Fed said in a summary of the meeting.

The Fed released a short summary of Tarullo's meeting, which lasted about one hour and 15 minutes and was held at the Federal Reserve Bank of New York.

The chief executives present included Goldman Sachs (GS) chief executive Lloyd Blankfein, J.P. Morgan Chase & Co. (JPM) chief executive Jamie Dimon and Bank of America Corp. (BAC) chief executive Brian Moynihan and James Gorman, chief executive of Morgan Stanley (MS).

The meeting partly focused on the tests of banks' financial health conducted by the Fed in mid-March, according to the central bank's summary. Some banks have been critical of the process, questioning gaps between their own internal estimates of their capital cushions and that of the central bank.

Tarullo said last month the central bank will consult with academics, analysts and banks to improve the stress test process. In a speech, he said "there should be some ways" for the Fed to better explain its mathematical models to banks.

The bank executives also were critical of numerous rules resulting from the 2010 Dodd-Frank financial overhaul. Particularly of concern was a proposal to limit the biggest banks' exposure to other firms and governments, which the banks contend could harm the financial system.

They were concerned about "the extent to which the proposed rules would overstate credit risk for certain transactions and would establish a more stringent credit exposure limit for the largest financial firms," the Fed said.

Tarullo told the banks that he would neither "respond or reply" to the banks' views, according to the Fed summary.

Also attending the meeting were Richard Davis, chief executive of U.S. Bancorp (USB) and Jay Hooley, chief executive of State Street Corp. (STT).

The bank chief executives were also concerned about several other aspects of Dodd Frank, the Fed said. Those include: the so-called Volcker rule, which limits their ability to trade for their own profit; a mandate that banks retain a portion of the risk for assets such as mortgages that are packaged into securities; and a provision that requires banks to stop relying on credit ratings.

-By Alan Zibel, Dow Jones Newswires; 202-862-9263; alan.zibel@dowjones.com

--Victoria McGrane contributed to this report.

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