The rupee appreciated 18 paise to 81.08 against the US dollar in early trade on Friday supported by a weak dollar in the overseas market.
Forex traders said weak domestic equities and foreign fund outflows weighed on the local unit and restricted the appreciation bias.
At the interbank foreign exchange, the domestic unit opened at 81.11 against the dollar, then gained further ground to touch 81.08, registering a rise of 18 paise over its previous close.
On Thursday, the rupee appreciated by 4 paise to close at 81.26 against the US dollar.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.01 per cent to 104.71.
Brent crude futures, the global oil benchmark, advanced 0.22 per cent to $87.07 per barrel.
In the domestic equity market, the 30-share BSE Sensex was trading 259.39 points or 0.41 per cent lower at 63,024.80. The broader NSE Nifty fell 71.60 points or 0.38 per cent to 18,740.90.
Foreign Institutional Investors (FIIs) were net sellers in the capital markets on Thursday as they offloaded shares worth ₹1,565.93 crore, according to exchange data.
Meanwhile, the collections from Goods and Services Tax (GST) grew by 11 per cent to about ₹1.46 lakh crore in November.
This is the ninth month in a row that the revenues have remained above the ₹1.4 lakh crore mark. However, the collection in November was the lowest since August.