The rupee depreciated by 6 paise to 71.17 against the US dollar in opening trade on Tuesday, tracking weak domestic equity market.
However, a weak dollar against other major currencies overseas and softening crude prices restricted the rupee's fall, dealers said.
At the interbank foreign exchange market, the local currency opened on a weak note at 71.17 and fell further to hit a low of 71.19 against the US dollar.
The domestic unit had settled at 71.11 against the American currency on Monday.
Market benchmark Sensex dropped over 200 points led by losses in index-heavyweights HDFC twins, Kotak Bank and ITC amid weak global cues.
After hitting an intra-day low of 41,301.63, the 30-share BSE index pared losses to trade 86.90 points or 0.21 per cent lower at 41,442.01.
The broader NSE too was trading 18.90 points, or 0.15 per cent, lower at 12,205.65.
Brent crude futures, the global oil benchmark, declined 0.49 per cent to USD 64.88 per barrel.
The dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.05 per cent to 97.56.
Meanwhile, foreign institutional investors remained net buyers in the capital markets, putting in Rs 5.87 crore on Monday, as per provisional data.
The 10-year Indian government bond yield was at 6.64 per cent.