Forex traders said the decline in the rupee was largely due to sharp drop in oil prices and stronger greenback which edged higher past the 100 level mark.
The rupee opened weak at 76.79 at the interbank forex market and during the day lost further ground and finally settled at 76.83, down 30 paise over its last close.
The rupee had settled at 76.53 against the US dollar on Monday.
During the session, the rupee witnessed high volatility and touched a high of 76.62 and a low of 76.84 against the US dollar.
WTI crude oil futures collapsed to negative; while Brent crude futures, the global oil benchmark, fell 14.47 per cent to USD 21.87 per barrel.
Domestic bourses were trading on a negative note on Tuesday.
Benchmark Sensex was down 1,034.07 points at 30,613.93, and Nifty shed 285.75 points to trade at 8,976.10.
The dollar index, which gauges the greenback’s strength against a basket of six currencies, rose by 0.25 per cent to 100.20.
Traders said investor sentiment remain fragile amid concerns over the impact of coronavirus outbreak on the domestic as well as global economy.
The number of cases around the world linked to the new coronavirus has crossed over 24.81 lakh. In India, nearly 18,600 coronavirus cases have been reported so far.