The rupee appreciated 30 paise to 75.65 against the US dollar in early trade on Tuesday tracking positive opening of domestic equities and weakness in the American currency.
Forex traders said a positive start of domestic stocks supported the local unit, while sustained foreign fund outflows and concerns over coronavirus outbreak weighed on the local unit.
At the interbank foreign exchange, the rupee opened at 75.69, then gained ground to touch 75.65, registering a rise of 30 paise over its previous close.
On Friday, rupee had settled at 75.95 against the US dollar.
Forex market was closed on Monday for Id-Ul-Fitr.
Traders said rupee tracked positive Asian equities and opened on a positive note.
"Asian shares are firm amid optimism that re-opening of businesses in several countries could fuel growth as investors look past the US-China tensions that has weighed on sentiments over the last week," Reliance Securities said in a research note.
Domestic bourses were trading on a positive note on Tuesday with the benchmark Sensex trading 280.45 points higher at 30,953.04 and broader Nifty rising 82.25 points to 9,121.50.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was trading 0.26 per cent down at 99.60.
Traders said investor sentiments remained fragile amid concerns over the impact of coronavirus outbreak on the domestic as well as global economy.
In India, the death toll due to COVID-19 rose to 4,167 and the number of cases climbed to over 1.45 lakh, according to Health Ministry data.
The number of cases around the world linked to the disease has crossed over 54.95 lakh and the death toll has topped 3.46 lakh.
Meanwhile, foreign institutional investors were net sellers in the capital market, as they sold equity shares worth Rs 1,353.90 crore on Friday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, rose 1.91 per cent to USD 36.21 per barrel.