Forex traders said foreign fund inflows and easing crude oil prices supported the rupee, while, factors like strong dollar and rising COVID-19 cases dragged down the local unit.
The rupee opened weak at 74.74 at the interbank forex market, then lost further ground to settle at 74.93 against the US dollar, 25 paise lower than its previous close.
It had closed at 74.68 against the US dollar on Monday.
In a highly volatile trading session, the rupee witnessed an intra-day high of 74.68 and a low of 74.97 against the US dollar.
The dollar index, which gauges the greenback's strength against a basket of six currencies, rose 0.26 per cent to 96.97.
On the domestic equity market front, the 30-share BSE benchmark Sensex was trading 7.66 points up at 36,494.94 and broader NSE Nifty fell 7.95 points to 10,755.70.
Foreign institutional investors were net buyers in the capital market as they purchased shares worth Rs 348.35 crore on Monday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, fell 0.58 per cent to USD 42.85 per barrel.
Meanwhile, the number of cases around the world linked to COVID-19 has crossed 1.16 crore and the death toll has topped 5.38 lakh.
In India, the death toll due the disease rose to 20,160 and the number of infections crossed the 7 lakh-mark, according to the health ministry. DRR ANS ANS