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.
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).