The card named 'Secure+' can be switched off by using a mobile phone application or Internet banking gateway or through the phone-banking application.
Besides, customers can also put limits on transactions.
At Rs 300 per year, it will cost a customer twice as much as a regular debit card offering to avail this card, said Jairam Sridharan, Axis Bank's president and head of retail lending and payments.
In case a customer has multiple cards of different lenders and loses his wallet, a single call to the bank's executive can help lock other banks' cards as well.
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Apart from that, those choosing this card will also get an enhanced personal accident insurance at Rs 5 lakh, he said.
He pointed to industry data showing only 10 per cent of the total 400 million cards were being used for transactions apart from ATM withdrawals.
"We want to decrease the usage of cash in the economy and such cards will help with that," he added.