"I think you should definitely see a reduction in base rates by most banks by Friday or thereabouts because most of them have also dropped their deposit rates," Puri told PTI.
He, however, refused to divulge his own bank's strategy or specify when its asset liability committee, which decides on rates, is meeting.
Finance Minister Arun Jaitley is meeting heads of the 27 state-run banks on Friday.
"The trigger is the reduction in rate by the RBI, loan demand being weak and lots of liquidity," he said, specifying the reasons which will prompt fresh round of base rate cuts.
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The RBI had cut its key rate by 0.25 per cent in the policy announcement last week and only SBI has reacted by announcing a rate cut of 15 bps to 9.7 per cent.
Puri acknowledged that the stance of competition in a market where everybody is vying for customers plays a part in cutting lending rates, along with the rates in competing money market instruments like certificate of deposits.
Even though a majority of banks had cut their lending rates following the RBI Governor's April tough talk, where he called the bank's posturing as nonsensical, Rajan had last week rued that banks are not doing enough, pointing out that the pace of deposit rate cuts has been faster.