He disclosed this after a meeting with the chiefs of PSU banks to review their financial performance and other parameters, including transmission of the RBI rate cuts so far this year.
"Some part of it (rate cut) have been passed on to customers, while some banks have not passed on. I feel over the next few days ... Some of the bankers felt that over the next few weeks, they would be in a position to work out greater cuts," the Minister said.
Some of the banks, Jaitley said, have expressed their inability to pass on the rate cuts on account of problems with their respective balance sheets and higher rates on small savings schemes.
However, he said that "the environment was optimistic. Since the movement in the banking sector appears to be for the better, this gives up a further hope of a greater recovery as far as economy is concerned.
A number of banks, including the largest public sector lender SBI, have cut their minimum lending rates after RBI reduced its policy rates by 0.25 per cent on June 2.
Since January, RBI has reduced repo (lending) rate by a total of 0.75 per cent in three tranches. The repo rate now stands at 7.25 per cent.
As regards the bad loans, Jaitley said it has come down in the January-March quarter and hoped that the situation would improve further with pick up in economy and higher public spending, especially in infrastructure sector projects.
"In quarter ending March 2015, NPAs had come down from 5.64 per cent to 5.2 per cent. One quarter does not indicate a pattern. So I would wait for some more time before realising what the pattern is. Banks are themselves of the assessment that it would take them 2-3 quarters to reach a somewhat more greater comfort level," he said.