The rupee on Tuesday settled 7 paise higher at 75.51 (provisional) against the US dollar tracking gains in the domestic equity market.
Forex traders said rupee traded in a narrow range as positive domestic equities supported the local unit, while foreign fund outflows and concerns over rising COVID-19 cases weighed on investor sentiment.
The rupee opened strong at 75.48 and settled for the day at 75.51 against the US dollar, up 7 paise over its previous close.
It had settled at 75.58 against the greenback on Monday.
During the four-hour trading session, the domestic unit saw an intra-day high of 75.45 and a low of 75.58 against the American currency.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, rose 0.09 percent to 97.62.
The 30-share BSE benchmark Sensex was trading 115.95 points higher at 35,077.47 and broader NSE Nifty rose 32.25 points to 10,344.65.
Foreign institutional investors were net sellers in the capital market as they sold shares worth Rs 1,937.06 crore on Monday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, fell 0.62 percent to $41.45 per barrel.
Meanwhile, the number of cases around the world linked to the disease has crossed 1.03 crore and the death toll has topped 5.05 lakh.
In India, the death toll due to COVID-19 rose to 16,893 and the number of infections spiked to 5,66,840, according to the health ministry.