At the interbank foreign exchange, the rupee opened at 75.89, then pared the initial losses to finally settle at 75.51 against the US dollar, registering a rise of 22 paise over its previous close.
During the day, the domestic unit hit an intra-day high of 75.49 and a low of 75.95 against the greenback.
On Monday, the rupee had settled at 75.73 against the US dollar.
The dollar index, which gauges the greenback's strength against a basket of six currencies, was trading 0.13 per cent lower at 100.11.
Foreign institutional investors were net buyers in the capital market, as they bought equity shares worth Rs 534.87 crore on Monday, according to provisional exchange data.
Meanwhile, domestic bourses were trading on a negative note with the BSE benchmark Sensex falling 446.90 points to 31,114.32 and the broader Nifty down 119.95 points at 9,119.25.
Brent crude futures, the global oil benchmark, rose 1.62 per cent to USD 30.11 per barrel. DRR BALBALBAL