Almost all world markets are closed today on account of the New Year's Day holiday.
A drop in local stocks and fresh dollar demand from importers weighed on the rupee. Persistent buying by foreign funds in domestic stocks limited the rupee's fall.
At the interbank foreign exchange market, the rupee opened lower at 61.83 a dollar from the previous close of 61.80 and moved in a range of 61.80 to 61.97. It ended at 61.90, a fall of 10 paise or 0.16 per cent.
"It was yet another range-bound session for the rupee...as most global markets have a bank holiday on the occasion of New Year," said Abhishek Goenka, CEO of India Forex Advisors.
The benchmark 30-share S&P BSE Sensex erased early gains and closed 30.20 points lower in a listless session.
"Today, Indian markets floated around yesterday's close as global markets remained closed for New Year's Day. Indian shares closed near yesterday's close with low volumes in a range-bound session. Taking cues from this, the rupee depreciated slightly," said Pramit Brahmbhatt, CEO of Alpari Financial Services (India).
"The markets are looking forward to the New Year 2014, where elections will be the major focus. The initial couple of months of the year are likely to witness inflows from FIIs, which will keep the rupee stable," Goenka said.
Foreign institutional investors bought a net Rs 309.70 crore of shares yesterday, according to provisional data from the stock exchanges. The US Federal Reserve's tapering of its stimulus programme is scheduled to start this month.
Forward dollar premiums remained weak on continued receipts by exporters.
The benchmark six-month forward dollar premium payable in June softened to 256-258 paise from 258-260 paise yesterday and far-forward contracts maturing in December eased to 495-497 paise from 496-498 paise.
The RBI fixed the reference rate for the dollar at 61.9335 and for the euro at 85.1235.
The rupee dropped further to 102.30 against the pound from 102.08 and fell to 85.08 per euro from 85.06. It moved up to 58.81 per 100 Japanese yen from 58.85.