The culture within big banks remains a possible source of financial instability seven years after the worst crisis since the Great Depression, and more work is needed to reform the underlying causes of Wall Street misconduct, a top Federal Reserve official said on Thursday.

New York Fed President William Dudley kicked off a conference of bankers and regulators with a warning that public trust in financial institutions has been compromised, and he urged Wall Street to focus less on seeking out "bad apples" and more on improving "apple barrels."

The central bank and other U.S. regulators have defended new laws and rules adopted in the wake of the 2007-2009 financial crisis as necessary, if sometimes cumbersome, to ensure it does not happen again.

More recently, as the world's largest banks were ensnared in rate-rigging scandals and other misconduct, Dudley and other officials have said ethics and culture, not just liquidity and capital, are a source of stability.

"Dodd-Frank apparently did little to curb misconduct––a possible source of systemic risk," Dudley said of the 2010 financial reform law.

"If the people managing capital cushions and liquidity buffers view these tools as sufficient mitigants for the costs of misconduct, or if powerful incentives encourage workarounds of the new regulations, then the connection between post-crisis reforms and greater financial stability becomes threatened," he said.