The rupee appreciated 12 paise to 78.94 against the US dollar in opening trade on Tuesday, supported by foreign fund inflows and a weak greenback against key rivals overseas.
Besides, softening crude oil prices strengthened domestic forex market sentiment, dealers said.
At the interbank foreign exchange, the rupee opened sharply up at 78.96 against the US dollar and gained further ground to quote at 78.94 in initial deals, registering a rise of 12 paise over the last close.
In the previous session, the rupee had closed at 79.06 against the US dollar.
The dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.22 per cent to 105.21.
Global oil benchmark Brent crude futures fell 1.05 per cent to $98.98 per barrel.
Foreign institutional investors were net buyers in the capital market on Monday, purchasing shares worth ₹2,320.61 crore, as per exchange data.