The rupee depreciated 3 paise to 82.76 against the US dollar in early trade on Tuesday, weighed down by a strong American currency .
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.
At the interbank foreign exchange, the domestic unit opened weak at 82.76 against the dollar, registering a decline of 3 paise over its last close.
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, the global oil benchmark, declined 1.11 per cent to USD 83.14 per barrel.
Lack of triggers is keeping volumes subdued, forex traders said, adding that over this week, focus will be on European flash PMIs and the US Fed minutes.
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.
Foreign Institutional Investors (FIIs) were net sellers in the capital markets on Monday as they offloaded shares worth Rs 158.95 crore, according to exchange data.