The rupee was trading in a narrow range against the United States dollar in opening trade on Thursday amid a rally in the equity markets.
At the interbank foreign exchange, the rupee witnessed range-bound trading in early deals. It opened at 79.22 against the U.S. dollar, then fell to 79.31, registering a decline of 6 paise over the last close.
It was moving in a tight range of 79.22-79.31 in the morning trade.
On Wednesday, the rupee rebounded by 38 paise to close at 79.25 against the U.S. currency.
The dollar index, which gauges the greenback's strength against a basket of six currencies, advanced 0.16 per cent to 105.36 after official data showed that U.S. inflation slowed down from a 40-year high in June to 8.5% in July on lower gasoline prices.
Meanwhile, global oil benchmark Brent crude futures gained 0.12% to $97.28 per barrel.
Forex traders said the rupee is likely to trade on a mixed note. Recovery in domestic markets from lower levels and FII inflows may support the local unit.
On the domestic equity market front, the 30-share Sensex was trading 582.67 points or 0.99% higher at 59,399.96 points, while the broader NSE Nifty was up 159.80 points or 0.91% to 17,694.55.
Foreign institutional investors remained net buyers in the capital market on Wednesday as they purchased shares worth ₹1,061.88 crore, as per exchange data.