Forex traders said rupee was trading in a narrow range as positive domestic equities and weak US currency supported the local unit, while rising coronavirus cases weighed on investor sentiment.
The rupee opened at 75.61 against the US dollar, registering a rise of 5 paise over its previous close.
It had settled at 75.66 against the greenback on Tuesday.
Traders said investor sentiments strengthened after top Chinese and Indian military commanders arrived at a consensus on the outstanding issues and agreed to take necessary measures to "cool down" the situation at their borders.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.01 per cent to 96.63.
The 30-share BSE benchmark Sensex was trading 205.06 points higher at 35,635.49 and broader NSE Nifty rose 64.50 points to 10,535.50.
Foreign institutional investors were net buyers in the capital market as they bought shares worth Rs 168.96 crore on Tuesday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, fell 0.38 per cent to USD 42.47 per barrel.
Meanwhile, investor sentiment remained fragile amid rising coronavirus cases across the world.
The number of cases around the world linked to the disease has crossed 92.40 lakh and the death toll has topped 4.76 lakh.
In India, the death toll due to COVID-19 rose to 14,476 and the number of infections spiked to 4,56,183, according to the health ministry. DRR ANS ANS