The rupee had weakened by 23 paise to end at 63.51 against the American currency on Wednesday on month-end dollar demand from oil companies and persisting selling by foreign funds in stocks.
The rupee had gained five paise to close at 63.25 against the dollar in on Monday's trade on fresh selling of the US currency by exporters amid bullish stocks.
The rupee has posted its biggest single-day fall in more than four months to end at 62.95 against the dollar.
Rajan said an interest rate cut won't by itself lead to higher economic growth
The RBI expects inflation in 2015 to hover around 6 per cent -- its target for January 2016 -- and sees risks to the target evenly balanced.
Rupee ends at 61.89 against the dollar, falls for second straight day.
The rupee had rebounded 15 paise to close at two-week high of 61.77 against the dollar at the Interbank Foreign Exchange on Friday.
The Reserve Bank of India kept interest rates unchanged at 8.0 percent on Tuesday as widely expected, staying focused on containing inflation while adopting a more dovish tone in response to the government's call for help to revive economic growth.
Analysts expect modest recovery in Indian economy.
Large state-run entities and business houses will not be allowed to set up small finance banks, which will have to comply with statutory reserve requirements.
The rupee had edged higher by four paise to end at 61.51 against the American currency in yesterday's trade on fresh selling of dollars by banks and exporters.
The dollar's weakness against other currencies overseas and a higher opening in the domestic equity market supported the rupee, forex dealers said.
The rupee had hit an intra-day low of 61.6750 on Friday, its lowest level since Oct. 17.
Traders are looking ahead at the consumer prices data due on Wednesday, amid rising expectation the Reserve Bank of India could opt for earlier-than-expected cuts in interest rates should inflation continue to ease.
The central bank will come out with fresh set of guidelines for companies applying for on-tap bank licence
The partially convertible rupee closed at 61.31/32 per dollar, unchanged from its Tuesday close.
The RBI's warnings signal its concern that unhedged firms could be a vulnerable link should global markets buckle.
In the offshore non-deliverable forwards, the one-month contract was at 61.58, while the three-month contract was at 62.18.
Rajan added "many" market participants were convinced that India could hit the RBI's target of bringing down consumer inflation to 6 percent by January 2016.
Forex dealers attributed the rupee's fall to increased demand for the US currency from importers and a lower opening in the domestic equity market.