A slowdown in capital inflows on account of the Christmas holiday also weighed in on the rupee amid a rise in local stocks, a forex dealer said.
At the interbank foreign exchange market, the rupee opened lower at 61.85 a dollar, also the day's high, from the previous close of 61.79.
It declined to a low of 62.17 before ending at 62.16, a fall of 37 paise or 0.60 per cent. In the previous three sessions, the rupee had risen by 35 paise.
The local currency is at the lowest level since closing at 62.36 on December 3.
Dealers attributed the fall in the rupee to dollar demand from importers, mainly oil refiners, to meet month-end requirements.
"After witnessing gains for the last three consecutive sessions, rupee was seen erasing the gains and weakening against the US dollar," said Abhishek Goenka, CEO of India Forex Advisors. "Fresh dollar demand seemed to have put pressure on the rupee."
The benchmark 30-share Sensex closed up 41.88 points or 0.20 per cent today. Foreign institutional investors bought shares worth a net Rs 40.67 crore on Tuesday, according to provisional data with the stock exchanges.
The dollar index was down 0.03 per cent in thin Christmas holiday trade.
"Today rupee traded weak against the dollar, with dollar buying pressure from oil companies," said Pramit Brahmbhatt, CEO of Alpari Financial Services (India).
Forward dollar premiums fell on fresh receipts by exporters.
The benchmark six-month forward dollar premium payable in May dropped to 227-1/2 to 229-1/2 paise from Tuesday's close of 232-234 paise. Far-forward contracts maturing in November dipped to 469-471 paise from 474-476 paise.
The RBI fixed the reference rate for the dollar at 61.9755 and for the euro at 84.7925.
The rupee turned negative to end at 101.81 against the pound from 101.13 previously and tumbled to 85.12 against the euro from 84.49.
The rupee declined to 59.34 per 100 Japanese yen from 59.25.