The rupee rose 11 paise to 74.91 per US dollar on Thursday amid positive domestic equities and weak US currency that supported the local unit.
Meanwhile foreign fund outflows and concerns over rising COVID-19 cases weighed on investor sentiment, traders said.
The rupee opened at 74.94 per US dollar, then gained further ground to touch 74.91 per dollar, up 11 paise over its previous close of 75.02 against the greenback on Wednesday.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.17 per cent to 96.26.
The 30-share BSE benchmark Sensex was trading 297.05 points higher at 36,626.06 and broader NSE Nifty rose 76.80 points to 10,782.55.
Foreign institutional investors were net sellers in the capital market as they sold shares worth Rs 994.87 crore on Wednesday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, rose 0.02 per cent to USD 43.30 per barrel.
Meanwhile, the number of cases around the world linked to the disease has crossed 1.20 crore and the death toll has topped 5.48 lakh.
In India, the death toll due to COVID-19 rose to 21,129 and the number of infections spiked to 7,67,296, according to the health ministry."