At 12:22 p.m. (0652 GMT), the three-day cash rate was at 9.45/9.50 percent, sharply up from 9.10/9.20 percent on Wednesday for two-day loans.
"We are seeing huge demand from private banks, as today is a reporting Friday," said a trader with a state-owned bank.
The number of business days being pruned this week on account of holidays was also causing the spurt in demand.
Indian markets were shut on Thursday on account of the Republic Day holiday.
The liquidity in the banking system stayed constrained, as reflected by the rise in banks' borrowings at the Reserve Bank of India's repo window for three-day loans, where bids rose to 1.59 trillion rupees ($32.06 billion) from 1.45 trillion rupees on Wednesday.
The liquidity situation is likely to improve next week following the RBI's move to reduce the banks' cash reserve ratio by 50 basis points, which takes effect on Saturday.
The reduction in the CRR, the share of deposits banks must hold with the central bank, will release around 320 billion of primary liquidity into the banking system, the RBI said.
Call money market volume was 135.32 billion rupees, down from Wednesday's volume of 196.68 billion rupees, data from the Clearing Corp of India showed.
In the collateralised borrowing and lending obligation (CBLO) market, volume was 147.24 billion rupees, down from 279.97 billion rupees on Wednesday.
The weighted average rate in the call money market was 9.10 percent, up from 8.94 percent on Wednesday. In the CBLO market, the average rate was 8.74 percent, up from 8.64 percent in the previous session.
In the inter-bank repo market, volume was 78.10 billion rupees, down from 99.06 billion rupees on Wednesday. The weighted average rate was 8.73 percent, up from 8.65 percent previously.