State-owned SBI made the largest cuts on shorter-term deposits. Annual rates for 7-45 days are being reduced to 5.0% from 5.75% while for 46 days to 179 days, the rate is getting cut to 5.75% from 6.25%.

For deposits of 180 days up to 10 years, the rate is being cut by up to 20 bps for individual retail customers and by up to 35 bps for the bulk segment, defined as a single deposit of 20 million rupees ($290,626) and above.

The rate changes will be effective Aug. 1.

The Reserve Bank of India, the central bank, has cut its key repo rate by 75 bps this year but commercial banks have mostly responded with just around 15-20 bps cuts in their key lending rates.

Banks often cite the high interest rates they say they need to offer on deposits as a hindrance to being able to cut lending rates.

"We are in a global low interest rate scenario. That is a clear fact. If the RBI reduces rates, SBI will reduce albeit with a lag and at a lesser rate," said Jagannadham Thunuguntla, head of research at Centrum Wealth Management.

The Indian government has already reduced interest rates on small savings schemes such as the National Savings Scheme, Public Provident Fund among others in late June by 10 bps.

Analysts said other banks may follow SBI's lead in cutting deposit rates but the timing and size of the moves will vary.

"In the current environment, people are looking at bank fixed deposits for safety of capital due to extreme risk-aversion sentiment," Thunuguntla said.

"But once that sentiment revives, the low interest rates on risk-free assets will act as a strong motivating factor for money to move into the more riskier assets."