Dollar demand from importers also weighed on the rupee, which declined for the third straight day, while some weakness in the US currency overseas and increased capital inflows restricted the fall, a forex dealer said.
At the interbank foreign exchange market, the rupee opened lower at 62.25 a dollar from yesterday's close of 62.09 and dropped further to a low of 62.48 as local stocks fell.
However, heavy portfolio investments by foreign funds and a fall in the dollar overseas later helped the rupee recover to a high of 62.07. It closed 62.14, a drop of five paise or 0.08 per cent. In three sessions, it has dipped by 41 paise.
The rupee is at the lowest level since December 3.
The US Fed will cut bond buying by USD 10 billion to USD 75 billion a month from January on signals the world's biggest economy is improving. The step may affect foreign capital inflows into local stocks.
"The immediate impact...was the domestic currency going weak against the dollar earlier...However, rupee was seen gaining later in the day on the back of dollar selling by bankers," said Abhishek Goenka, CEO of India Forex Advisors.
The benchmark 30-share S&P BSE Sensex today dropped 151.24 points or 0.73 per cent.
"US Fed decision to start tapering and panic buying from oil importers kept rupee under pressure. However, at 62.41-62.42 levels, nationalised banks started selling dollars, likely on behalf of RBI, which was aimed at reducing volatility," the chief dealer at a state-owned bank said.
RBI Governor Raghuram Rajan yesterday said state-run oil marketing companies have about USD 7 billion in pending settlements after they availed of the central bank's special swap window to meet their dollar needs.
Foreign institutional investors bought shares worth a net Rs 1,198.60 crore yesterday, according to provisional data from the stock exchanges. Their net purchases today stood at Rs 2,264.11 crore.
"The unwinding of Fed stimulus is generally seen as positive for the dollar," said Pramit Brahmbhatt, CEO of Alpari Financial Services (India).
Finance Minister P Chidambaram said today the government is of the view that the markets had already factored in the US Federal Reserve's decisions and, therefore, is not likely to be surprised by these "moderate changes."
"Fed's decision to taper means less amount of money flow in global and emerging markets, which was rupee-negative," said Harihar Krishnamoorthy, Head - Treasury at FirstRand Bank. "Exporters interest came as the forward premium were at attractive levels, which helped the rupee."
Forward dollar premiums dropped sharply on sustained receipts by exporters.
The benchmark six-month forward dollar premium payable in May tumbled to 235-237 paise from 243-245 paise yesterday and far-forward contracts maturing in November plunged to 474-1/2 to 476-1/2 paise from 486-1/2 to 488-1/2 paise.
The RBI fixed the reference rate for the dollar at 62.3800 and for the euro at 85.2945.
The rupee declined further to 101.79 against the pound from 101.52 previously and recovered to 85.03 per euro from 85.40. It bounced back to 59.69 per 100 Japanese yen from 60.32.