Forex traders said heavy buying in domestic equity market, sustained foreign fund inflows and upbeat risk appetite supported the rupee.
The rupee opened on a strong note at 75.04 at the interbank forex market, up 32 paise over its last close.
It had settled at 75.36 against the US dollar on Tuesday.
"Most Asian currencies have started with gains against the US Dollar this morning and could lend support to the domestic currency," Reliance Securities said in a research note.
Forex traders said global risk sentiment is holding up as coronavirus curve seems to plateau in western countries.
"Overall risk sentiment is positive. So far there are no signs of a second wave despite economies opening up in Europe and the US. The new cases curve seems to be plateauing," said Abhishek Goenka, Founder and CEO IFA Global.
The number of cases around the world linked to the disease has crossed 63.78 lakh and the death toll has topped 3.80 lakh.
Meanwhile, in India, the death toll due to COVID-19 rose to 5,815 and the number of the number of infections rose to 2,07,615, according to the health ministry.
On the equities front, the 30-share BSE benchmark Sensex was quoting 361.71 points higher at 34,187.24 and broader Nifty rose 107.80 points to 10,086.90.
Foreign institutional investors were net buyers in the capital market, as they bought equity shares worth Rs 7,498.29 crore on Tuesday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, rose 1.04 per cent to USD 39.98 per barrel.
The dollar index, which gauges the greenback's strength against a basket of six currencies, fell by 0.28 per cent to 97.39. DRR ANS ANS