At the interbank foreign exchange, the rupee opened at 71.77, showing a decline of just 1 paise over its previous closing.
The domestic unit however, gained some momentum and touched a high of 71.70 against the dollar, showing a rise of 6 paise over its last close.
The Indian rupee on Thursday had closed at 71.76 against the US dollar.
Traders said rupee is trading in a narrow range as market is awaiting fresh cues on the potential US-China trade deal.
Meanwhile, brent crude futures, the global oil benchmark, fell 0.58 per cent to USD 63.61 per barrel.
Foreign institutional investors remained net buyers in the capital markets, as they purchased shares worth Rs 5,023.54 crore on Thursday, as per provisional data.
Domestic bourses opened on a cautious note on Friday with benchmark indices Sensex trading 13.98 points up at 40,589.15 and Nifty down 9.50 points to 11,958.90 .
The dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.04 per cent to 97.95.
The 10-year government bond yield was at 6.50 per cent in morning trade. DRR DRR