Forex traders said a positive start of domestic stocks supported the local unit, while sustained foreign fund outflows and concerns over coronavirus pandemic weighed on the local unit.
At the interbank foreign exchange, the rupee opened at 75.60, registering a rise of 6 paise over its previous close.
On Tuesday, the rupee had settled at 75.66 against the US dollar.
Domestic bourses were trading on a positive note with the benchmark Sensex trading 281.53 points higher at 30,477.70 and broader Nifty rising 87.20 points to 8,966.30.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was trading 0.09 per cent higher at 99.46.
Traders said investor sentiment remained fragile amid concerns over the impact of coronavirus outbreak on the domestic as well as global economy.
Globally, over 48.97 lakh people have been infected by the virus and over 3.23 lakh have died.
In India, the death toll due to COVID-19 rose to 3,303 and the number of cases climbed to 1.06 lakh, according to the health ministry.
Meanwhile, foreign institutional investors were net sellers in the capital market as they sold equity shares worth Rs 1,328.31 crore on Tuesday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, rose 0.81 per cent to USD 34.93 per barrel. DRR ANS ANS