The rupee appreciated 16 paise to 75.87 per dollar on Tuesday amid sustained foreign fund inflows and rising domestic equity market.
Lower crude prices also helped the local unit to strengthen its ground, boosting investor confidence.
The rupee opened strong at 75.86 against the US dollar. However, it soon edged marginally lower to 75.87 per dollar, rising 16 paise over its previous close of 76.03 against the greenback on Monday.
Meanwhile, the equity benchmark Sensex was trading 145.74 points, or 0.42 per cent, up at 35,057.06. Similarly, NSE Nifty rose 46.15 points, or 0.45 per cent, to 10,357.35.
Foreign institutional investors remained net buyers in the capital market as they bought shares worth Rs 424.21 crore on Monday, according to provisional exchange data.
The dollar index, which gauges the greenback's strength against a basket of six currencies, was trading marginally higher by 0.03 per cent to 97.06.
Brent crude futures, the global oil benchmark, declined 0.19 per cent to USD 43.00 per barrel.
India's COVID-19 tally climbed to 4,40,215 on Tuesday while the death toll rose to 14,011 with 312 new fatalities, according to the Union Health Ministry data.