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 to 75.97 against the US dollar, down 13 paise over its last close.
It had settled at 75.84 against the US dollar on Friday.
"There has been a fresh spike in coronavirus cases in Tokyo, Beijing and the US and this is weighing on risk sentiment," said Abhishek Goenka, Founder and CEO, IFA Global.
Goenka further said that India's forex reserves crossed the USD 500 billion, rising USD 8 billion in the week ended June 5.
"This shows how aggressively the Reserve Bank of India has been absorbing Inflows. The reserve cushion would give the central bank ammunition in containing volatility during bouts of outflows," he said.
Meanwhile, the 30-share BSE benchmark Sensex was trading 387.08 points lower at 33,393.81 and the broader NSE Nifty fell 105.95 points to 9,866.95.
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 2.12 per cent to USD 37.91 per barrel.
The dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.28 per cent to 97.04.
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 79.12 lakh and the death toll has topped 4.33 lakh. DRR DRR ANS ANS