The Fed might for instance look closer at the risk of common exposures among firms in the annual model run known as "stress tests," which Tarullo defended as the core element of the Fed's oversight of the banking sector.

"I expect that we will devote more attention to developing the macroprudential elements of the stress tests," Tarullo said in the text of a speech he gave in Boston.

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The Fed requires banks to submit capital plans that show whether they can withstand adverse economic scenarios, and can stop the banks from raising dividends or other shareholder payouts if it deems them insufficient.

This year it rejected plans by Citigroup to buy back $6.4 billion of shares and boost dividends, and also objected to plans from the U.S. units of three European banks: HSBC, RBS and Santander.

It was the second time in three years that Citi flunked, and a blow to Chief Executive Michael Corbat, who has been working hard to cultivate closer relationships with regulators since taking the company's reins in 2012.

The Fed has identified the stress tests as the cornerstone of their oversight of banks. The European Central Bank also is conducting its own stress tests in Europe as it takes on responsibility for supervising banks this year.

Tarullo said the Fed might start looking at whether there could be knock-on effects from banks that started rapidly selling assets during a crisis, and whether they would still have access to credit in times of stress.

But there was no desire to make the tests harder each year, Tarullo said. If that appeared to be the case, it was because banks had a long way to go when the Fed started using the tests after the financial crisis that peaked in 2008, he said.

The Fed also does not have a number in mind for how many banks should fail the test, Tarullo said.

"This is not a PGA tournament — there is no foreordained cut that some participants will miss," he said, using a reference to the way professional golf tournaments are set up.

Tarullo also defended against the idea the stress tests are an opaque process, saying that while the Fed would not disclose the models it used, it had put a system in place to independently validate the models.

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