Dollar sales by exporters and some weakness in the US currency overseas also supported the rupee.
The 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 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 yesterday's close, which helped the rupee," said Pramit Brahmbhaat, CEO at Alpari Financial Services (India).