Forex traders said risk appetite has waned amid fresh cases of COVID-19 globally.
The rupee opened weak at 75.93 at the interbank forex market. It fell further and finally settled for the day at 76.03 against the US dollar, down 19 paise over its last close.
It had settled at 75.84 against the US dollar on Friday.
During the four-hour trading session, the rupee witnessed an intra-day high of 75.93 and a low of 76.15.
Meanwhile, the 30-share BSE benchmark Sensex was trading 472.54 points lower at 33,308.35 and the broader NSE Nifty fell 130.65 points to 9,842.25.
Foreign institutional investors were net sellers in the capital market as they sold shares worth Rs 1,311.49 crore on Friday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, fell 0.85 per cent to USD 38.40 per barrel.
The dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.13 per cent to 97.19.
Meanwhile, investor sentiment remained fragile amid rising coronavirus cases across the world.
India saw a jump of over 11,000 cases for the third consecutive day on Monday, taking the total number of infections to over 3.32 lakh, while the death toll rose to 9,520 with 325 more fatalities, the Health Ministry said.
Globally, the number of cases linked to the disease has crossed 79.25 lakh and the death toll has topped 4.33 lakh. DRR DRR ANS ANS