Mr Mundra added recent inspections by the RBI had found recurrences of certain violations such as those related to "know your customer" (KYC) rules as well as discrepancies between assets held and provisioning. He did not provide specific details.
The official also urged the committees to pre-emptively address potential risks rather having to fix "the number of deficiencies identified by the supervisor."
The comments, in a speech to ICICI Bank Ltd officials on Tuesday uploaded by the Reserve Bank of India, come as the apex bank pushes to clean up lenders in a bid to revive lending in a sector still saddled with a pile of non-performing loans.
"Even in the matters of compliance, some ACBs (audit committee of boards) are found lacking in proper monitoring," Mr Mundra said in his speech.
"I urge the ACBs to ask uncomfortable questions," he added. "RBI's dependence on auditors is only going to increase and a very competent ACB will provide a great deal of supervisory comfort to us."
The RBI had previously been urging banks to set up early warning systems to detect bad loans, frauds and to be mindful of the inter-connected nature of the financial system.
As of the end of September, stressed assets, meaning loans which are recoverable despite being overdue, reached 10.7 per cent of total bank assets.
($1 = 61.5900 rupees)
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