The statement comes against the backdrop of the revelation of fraud in Punjab & Maharashtra Cooperative (PMC) Bank involving the Housing Development and Infrastructure Limited (HDIL).
"There are rumours in some locations about certain banks including cooperative banks, resulting in anxiety among the depositors. RBI would like to assure the general public that Indian banking system is safe and stable and there is no need to panic on the basis of such rumours," the RBI said in a tweet.
Among other violations, the PMC bank opened a number of dummy accounts to replace the stressed accounts held by Wadhawans-led HDIL.
In a letter to Reserve Bank of India (RBI), the tainted bank's now-suspended Managing Director Joy Thomas admitted to large-scale wrong-doings and the cover-up exercise.
He said that in 2011, the size of the bank was around 57 branches, with deposits of Rs 2,824 crore and advances of Rs 2,000 crore. The exposure of the HDIL group was then Rs 1,026 crore.
"Had we classified then as non-performing asset, we would have to stop charging interest on these accounts and we could have made losses. The growth part of the bank would have got hampered."
Thomas, however, said that the bank is still optimistic about the repayment plan of the HDIL group and the group always promised to clear the dues and gave backup security to back their loans.
Last week, the RBI barred the PMC Bank from carrying out the majority of its routine business transactions for a period of six months, sparking panic among the depositors and sending shock-waves in the city banking and business circles on Tuesday.
Thomas, who was then the MD, said the bank had been put under regulatory restrictions by RBI owing to irregularities disclosed to the apex bank.
( With inputs from IANS )