Besides, a higher dollar overseas following unexpectedly better US housing data for April, weighed on the rupee.
The dollar index was up by 0.30 per cent against a basket of six major global rivals in late Asian trade today.
However, firm domestic stocks and renewed capital inflows restricted the fall in the rupee, a forex dealer said.
At the Interbank Foreign Exchange (Forex) market, the domestic unit commenced weak at 63.78 per dollar from overnight close of 63.67 and immediately touched a low of 63.88 before ending at 63.82, disclosing a fall of 15 paise or 0.24 per cent.
Yesterday, it had appreciated by five paise or 0.08 per cent.
The domestic currency moved in a range of 63.66 and 63.88 during the day.
The benchmark S&P BSE Sensex ended higher by 191.68 points, or 0.68 per cent, after yesterday's fall of nearly 42 points.
Foreign Portfolio Investors (FPIs), who were sellers from past few days, bought shares worth Rs 48.06 crore yesterday, as per provisional data.In the forward market, the premium moved down further on sustained receivings by exporters.
The benchmark six-month premium payable in October fell to 204.5-206.5 paise from 207-209 paise yesterday while forward contracts maturing in April 2016 also declined to 426-428 paise from 430-432 paise.
The Reserve Bank of India fixed the reference rate for the dollar at 63.8655 and for the euro at 70.7310.
The rupee fell against the pound sterling to 99.00 from 98.61 yesterday but recovered against the euro to 70.80 from 71.21 previously.
Meanwhile, the rupee also firmed up against the Japanese currency at 52.75 per 100 yen from 53.00 yesterday.
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