The rupee appreciated 7 paise to 79.84 against the US dollar in early trade on Tuesday in line with a positive trend in domestic equities.
However, higher oil prices and month-end dollar demand could restrict the gains for the local unit, forex traders said.
At the interbank foreign exchange, the rupee opened at 79.92 against the American dollar and touched 79.84 in initial deals, registering a gain of 7 paise over the last close.
On Monday, the rupee closed at 79.91 against the US dollar.
The rupee opened on a flat note after Monday's volatile session in which RBI had intervened to support the currency amid a fall in equities and a rise in the dollar index, according to experts.
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Asian currencies are generally down as the market digests US Federal Reserve chief Jerome Powells' hawkish tone on interest rates on Friday.
The dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.06 per cent to 108.76.
Global oil benchmark Brent crude futures fell 0.77 per cent to $104.28 per barrel.
On the domestic equity front, the 30-share Sensex was trading 485.2 points or 0.84 per cent higher at 58,457.82 points while the broader NSE Nifty advanced 154.10 points or 0.89 per cent to 17,467.00 points.
Foreign institutional investors remained net sellers in the capital market on Monday, offloading shares worth Rs 561.22 crore, as per exchange data.
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