The government has asked RBI and banks to provide details of the data breach and also banks' preparedness to deal with cyber crimes.
"Have sought a report in the debit card issue. The idea is to contain the damage," Jaitley told reporters here.
Several banks, including state-owned SBI, have recalled a number of cards, while many others blocked the ones suspected to have been compromised and asked their customers to change PIN (personal identification number) before use.
Fraudulent withdrawals have been reported from 19 banks so far while complaints have been received from a few banks that their customers' cards were used fraudulently abroad, mainly in China and the US while the customers were in India.
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Meanwhile, Economic Affairs Secretary Shaktikanta Das said there is no need to panic over the feared security breach and promised swift action in the matter.
SBI is said to have recalled around 6 lakh cards while others like Bank of Baroda, IDBI Bank, Central Bank and Andhra Bank have replaced debit cards of several customers as a pre-emptive measure.
The suspected security breach happened through a malware in the systems of Hitachi Payments Services, which serves ATM network of Yes Bank and also some white-label ATMs.