Forex traders said positive domestic stock market, sustained foreign fund inflows, weak American currency and upbeat risk appetite supported the rupee.
The rupee opened on a strong note at 75.38 at the interbank forex market, up 19 paise over its last close.
It had settled at 75.57 against the US dollar on Thursday.
On the equities front, the 30-share BSE benchmark Sensex was quoting 87.70 points higher at 34,068.40 and broader Nifty rose 42 points to 10,071.10.
Foreign institutional investors were net buyers in the capital market, as they bought shares worth Rs 2,905.04 crore on Thursday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, rose 0.55 per cent to USD 40.21 per barrel.
The dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.01 per cent to 96.67.
Meanwhile, the number of cases around the world linked to the disease has crossed 66.35 lakh and the death toll has topped 3.91 lakh.
In India, the death toll due to COVID-19 rose to 6,348 and the number of infections rose to 2,26,770, according to the health ministry. DRR DRR ANS ANS