The rupee was trading in a narrow range against the US 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 US 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 US 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 US inflation slowed down from a 40-year high in June to 8.5 per cent in July on lower gasoline prices.
Meanwhile, global oil benchmark Brent crude futures gained 0.12 per cent 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 per cent higher at 59,399.96 points, while the broader NSE Nifty was up 159.80 points or 0.91 per cent 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.