In early trade on Tuesday, the rupee fell 3 paisa to 82.76 against the US dollar as a result of the strong greenback.
Forex traders said the rupee is trading in a narrow range as a positive trend in domestic equities and easing crude oil prices supported the local unit and restricted the fall.
The domestic unit opened weak at the interbank foreign exchange, down 3 paise from its previous close, at 82.76 against the dollar.
In the previous session on Monday, the rupee settled at 82.73 against the dollar.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, rose 0.19 per cent to 104.05.
Brent crude futures fell 1.11 percent to USD 83.14 per barrel, the global oil benchmark.
According to forex traders, low volume is being caused by a lack of triggers, and this week, attention will be focused on the US Fed minutes and the European flash PMIs.
In the domestic equity market, the 30-share BSE Sensex was trading 104.11 points or 0.17 per cent higher at 60,795.65. The broader NSE Nifty advanced 14.25 points or 0.08 per cent to 17,858.85.
According to exchange data, Foreign Institutional Investors (FIIs) sold shares worth Rs 158.95 crore on Monday, making them net sellers in the capital markets.
With inputs from Agencies.
