US Dollar sales by exporters and some weakness in the US currency overseas also supported the rupee.
The Indian rupee opened lower at 62.40 a dollar from the previous close of 62.14 at the interbank foreign exchange market and dropped to 62.45 on sustained dollar demand from importers, mainly oil refiners.
The local currency rebounded to a high of 62.01 on fresh dollar selling by exporters and strong local stocks. It ended at 62.04, a rise of 10 paise or 0.16 per cent. In the three previous sessions, it had fallen 41 paise.
"The domestic currency opened on a lacklustre note today as all the Asian currencies were trading weak against the US dollar," said Abhishek Goenka, CEO of India Forex Advisors.
"Rupee was seen gaining later during the session on the back of dollar selling by bankers."
The benchmark 30-share S&P BSE Sensex today shot up 371.10 points or 1.79 per cent.
Foreign institutional investors bought shares worth a net Rs 2,264.11 crore yesterday, according to provisional data. Their net purchases today were Rs 990.19 crore.
"The dollar index, which tracks the performance of the greenback versus a basket of six other major units, opened on a strong note but during the day it weakened and at present is trading near yesterdays close, which helped the rupee," said Pramit Brahmbhaat, CEO at Alpari Financial Services (India).
Forward dollar premiums dipped further on sustained receipts by exporters.
The benchmark six-month forward dollar premium payable in May dropped to 229-1/2 to 231-1/2 paise from the overnight close of 235-237 paise and far-forward contracts maturing in November slumped to 466-1/2 to 468-1/2 paise from 474-1/2 to 476-1/2 paise.
The RBI fixed the reference rate for the dollar at 62.2420 and for the euro at 84.8774.
The rupee turned positive to end at 101.34 against the pound from 101.79 yesterday and improved to 84.70 per euro from 85.03. It remained firm to settle at 59.41 per 100 Japanese yen from 59.69.