The rupee gained 3 paise to 82.81 against the US dollar in early trade on Tuesday, supported by foreign fund inflows and a positive trend in domestic equities.
Forex traders said the rupee is trading in a narrow range as the broad strength of the greenback is restricting the appreciating bias.
At the interbank foreign exchange market, the domestic unit opened at 82.82 against the dollar and then rose to 82.81, registering a gain of 3 paise over its previous close.
On Monday, the rupee closed at 82.84 against the US currency.
The rupee is likely to trade in the 82.65-82.95 range with sideways price action, IFA Global Research Academy said in a research note, adding that the Reserve Bank of India is likely to continue supporting the local unit.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, rose 0.07 per cent to 103.27.
Brent crude futures, the global oil benchmark, advanced 0.36 per cent to $76.26 per barrel.
Foreign Institutional Investors (FIIs) were net buyers in the capital market on Monday as they purchased shares worth Rs 922.89 crore, according to exchange data.