The rupee appreciated 7 paise to 79.74 against the US dollar in early trade on Thursday, 14 July, as a positive trend in domestic equities supported the local unit.
However, a strong American currency overseas and forex outflows restricted the rupee's gain, dealers said.
At the interbank foreign exchange, the rupee opened at 79.72 against the American dollar, then went lower to trade at 79.74 against the greenback in early deals, registering a gain of 7 paise over the last close.
In the previous session, the rupee had closed at an all-time low of 79.81 against the greenback.
The local unit was moving in a tight range of 79.71 to 79.74 in early trade.
On the domestic equity front, the 30-share Sensex was trading 134.45 points or 0.25 percent higher at 53,648.60, while the broader NSE Nifty advanced 40.15 points or 0.25 percent to 16,006.80.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, gained 0.30 per cent to 108.30.
Global oil benchmark Brent crude futures rose 0.57 percent to USD 100.14 per barrel.
Foreign institutional investors remained net sellers in the capital market on Wednesday, offloading shares worth Rs 2,839.52 crore, as per exchange data.
Meanwhile, the US consumer price index rose to a multi-year high of 9.1 percent in June, fuelling speculation that the Federal Reserve will raise interest rates aggressively to tame soaring prices.