Forex traders said positive domestic equities supported the rupee, but factors like rising coronavirus cases and border tension with China weighed on the local unit.
The rupee opened at 76.28 against the US dollar, then fell further to 76.29 against the US dollar, down 15 paise over its previous close.
It had settled at 76.14 against the greenback on Thursday.
"Most Asian currencies were weak against the greenback this morning as the US dollar extended gains supported by safe haven appeal and could weigh on the domestic unit," said Abhishek Goenka, Founder and CEO, IFA Global.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.03 per cent to 97.38.
The 30-share BSE benchmark Sensex was trading 103.97 points higher at 34,312.02 and broader NSE Nifty rose 34.70 points to 10,126.35.
Foreign institutional investors were net buyers in the capital market as they bought shares worth Rs 366.57 crore on Thursday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, rose 0.89 per cent to USD 41.88 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 84.64 lakh and the death toll has topped 4.53 lakh.
In India, the death toll due to COVID-19 rose to 12,573 and the number of infections spiked to 3,80,532, according to the health ministry. DRR ANS ANS