At the interbank foreign exchange, the domestic unit opened weak at 81.94 against the dollar, then slipped further to 82.09, registering a fall of 24 paise over its previous close.
In the previous session on Monday, the rupee had settled down by 52 paise at 81.85 against the dollar.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.07 per cent to 105.22.
Brent crude futures, the global oil benchmark, advanced 0.94 per cent to USD 83.46 per barrel.
In the domestic equity market, the 30-share BSE Sensex was trading 353.44 points or 0.56 per cent lower at 62,481.16. The broader NSE Nifty fell 99.30 points or 0.53 per cent to 18,601.75.
Foreign Institutional Investors (FIIs) were net sellers in the capital markets on Monday as they sold shares worth Rs 1,139.07 crore, according to exchange data.
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