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.
Roy and his associates were jailed in March after he failed to appear at a contempt hearing in the long-running dispute with the capital markets watchdog over the company's failure to repay billions of dollars to investors who were sold outlawed bonds.
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.
The bank adds it expects Modi to fight inflation through administrative measure
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.
In the latest large opinion poll, the opposition Bharatiya Janata Party and its allies were forecast to win a narrow majority in the 543-seat lower house of parliament, compared with previous surveys predicting that they would fall short.
The domestic currency had gained a massive 47 paise to close at 60.60 on Friday amid heavy selling of the US currency by corporates, exporters and banks.
Industrial countries cannot at this point wash their hands off developing economises and say we will do what we need to, and you do the adjustment you need to, says RBI Governor.
India's consumer inflation should ease in the next two months, and will fall to 8 per cent by the end of the year, says RBI Governor Raghuram Rajan.
Bond yields have risen since the Reserve Bank of India raised interest rates for a second consecutive month on October 29.
The rupee has already shed around 3.3 percent over the last five sessions.
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