At the interbank foreign exchange the rupee opened at 71.80 then gained further ground and touched a high of 71.78, registering a rise of 18 paise over its previous close.
On Thursday, rupee had settled for the day at 71.96 against the US dollar.
The domestic unit however could not hold on to the gains and was trading at 71.86 against the dollar at 1008 hrs.
Higher opening in domestic equities supported the local unit, forex traders said.
Domestic bourses opened on a positive note on Friday with benchmark indices Sensex trading 212.50 points higher at 40,498.98 and Nifty up 53.20 points at 11,925.30.
The dollar index, which gauges the greenback's strength against a basket of six currencies, fell marginally by 0.03 per cent to 98.13.
Market participants, however, said sustained foreign fund outflows and rising crude oil prices weighed on local currency.
Foreign institutional investors (FIIs) remained net sellers in the capital market, pulling out Rs 562.05 crore on Thursday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, rose 0.43 per cent to trade at USD 62.55 per barrel.
The 10-year government bond yield was at 6.52 per cent in morning trade. DRR DRR