The Indian rupee appreciated by 8 paise to 75.51 against the US dollar in early trade on Tuesday tracking positive opening in domestic equities.
Forex traders said the rupee is trading in a narrow range as the higher opening in domestic equities supported the local unit, while sustained foreign fund outflows and strengthening of the American currency weighed on it.
At the interbank foreign exchange the rupee opened at 75.52, then gained ground and touched 75.51, registering a rise of 8 paise over its previous close.
On Monday, rupee had settled at 75.59 against the US dollar.
Traders said investor sentiments remain fragile amid concerns over the impact of coronavirus outbreak on the domestic as well as global economy.
The number of deaths around the world linked to the new coronavirus has crossed over 37,000. In India, nearly 1,100 coronavirus cases have been reported so far.
Meanwhile, domestic bourses opened on a positive note on Tuesday with benchmark indices Sensex trading 475.89 points higher at 28,916.21 and Nifty up by 156.65 points at 8,437.75.
Foreign institutional investors (FIIs) remained net sellers in the capital market, as they sold equity shares worth Rs 4,363.61 crore on Monday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, rose 1.71 per cent to USD 23.15 per barrel.
Meanwhile, the dollar index, which gauges the greenback's strength against the basket of six currencies was trading 0.17 per cent higher at 99.34.
The 10-year government bond yield was at 6.10 per cent in morning trade.