The partially convertible rupee closed at 61.45/46 per dollar, weaker from Wednesday's 61.35/36.
In the offshore non-deliverable forwards, the one-month contract was at 61.56/66, while the three-month contract was at 62.16/26.
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The RBI's warnings signal its concern that unhedged firms could be a vulnerable link should global markets buckle.
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.
The big test will come at the end of March when the fiscal year ends and banks tend to hold on to cash.
The rupee appreciated by three paise to close at one-week high of 60.81 against the US dollar in the previous session on sustained dollar selling by exporters and capital inflows.
Rajan also said the RBI had reduced the current account deficit "substantially".
India's macroeconomic indicators are improving and inflation has been coming down consistent with the central bank's forecast, but Asia's third-largest economy needs investment growth to pick up, he added.
The rupee bounced back by 26 paise to end at 59.93 against the American currency on Friday as exporters and some banks sold dollars.
The rupee had revisited the near 2-month low of 60.55 per dollar earlier in the session.
The rupee had closed at 60.1550/1650 per dollar on Monday.
Increased selling of the dollar by banks and exporters amid sustained foreign capital inflows supported the rupee.
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The moves by the RBI, announced late on Wednesday, should increase supplies of gold and brighten the earnings outlook for jewellery makers after the government took tough measures to curb imports last year, analysts said.
A higher opening in the domestic equity market also supported the rupee but dollar's gain against other currencies overseas limited the rise of domestic unit, forex dealers said.
The rupee had retreated four paise from its 11-month high levels to close at 58.63 against the dollar on Tuesday on fresh demand for the US currency from importers, amid some profit- booking in stocks.
He said the total capital requirement for state-run banks is Rs 455 billion ($7.6 billion) in 2014/15 fiscal year, much lower than the Rs 113 billion provided for recapitalisation in the interim budget in February.
The currency got support from dollar flows into local equities and greenback sales from state-run lenders.
Forex dealers said besides selling of the American currency by exporters and banks, gains in other Asian currencies against the dollar and a higher opening in the domestic stock market also supported the rupee.