The rupee depreciated 15 paise to 76.40 against the US dollar in opening trade on Tuesday, amid strengthening American currency overseas and volatility in domestic equities.
Forex traders said the weakness in the rupee was largely due to muted domestic equities and strengthening of the US dollar. Moreover, rising coronavirus cases in the country also weighed on the local unit.
The rupee opened weak at 76.33 at the interbank forex market and then fell further to 76.40, down 15 paise over its last close.
The rupee had settled at 76.25 against the US dollar on Monday.
Forex traders said market participants were concerned that the sharp rise in coronavirus cases could weigh on the economy.
In India, the death toll due to COVID-19 rose to 934 and the number of cases climbed to 29,435 in the country on Tuesday, according to the Union Health Ministry.
Meanwhile, the number of cases around the world linked to the disease has crossed over 30 lakh and the death toll has topped 2 lakh.
Domestic bourses were trading on a muted note with benchmark indices Sensex trading 14.22 points up at 31,757.30 and Nifty higher by 4.55 points at 9,286.85.
Foreign institutional investors remained net sellers in the capital market, as they sold equity shares worth Rs 916.42 crore on Monday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, fell 5.05 per cent to USD 18.98 per barrel.
The dollar index, which gauges the greenback's strength against a basket of six currencies, rose by 0.10 per cent to 100.13.