ICICI Bank Managing Director and CEO K V Kamath on Tuesday did not rule out the possibility of interest rates going up in the immediate run and said the rates may not have peaked yet.

"We cannot say if interest rates have peaked or not. We have to see what happens on inflation front and what policy steps are taken (by the RBI)," Kamath said when asked about outlook on interest rates.

Last week, State Bank of India Chairman O P Bhatt had said interest rates have almost peaked, which is unlikely to change unless RBI took any further action.

"It (interest rate) has peaked or near peaked unless there is any further cause of action by external factors or RBI," he had said.

Last month, the Reserve Bank had tightened the money supply by increasing the short-term lending (repo) rate and the mandatory deposits to be parked with it (CRR) by 50 and 25 basis points respectively to tame inflation.

The RBI had hiked CRR for the fourth time and repo rate third time during the current fiscal. 

As a fallout of policy rate hike, most banks, including State Bank of India, ICICI Bank, Punjab National Bank and Bank of Baroda, increased lending and deposit rates up to one per cent.

After the hike, prime lending rate of most of the banks went up to 14 per cent.

Bhatt had said oil prices are softening, monsoons are good, commodity prices especially of steel seem to have peaked and demand pull because of Olympics also seems to be over.

Global economy is slowing down and there seems to be enough reasons that interest rates have peaked or near peaked, he had said.