At the interbank foreign exchange, the rupee opened at 71.26 then rose to 71.22 against the dollar, showing a rise of 5 paise over its previous closing.
The Indian rupee on Tuesday had closed at 71.27 against the dollar.
Forex market was closed on Wednesday on account of Christmas.
Forex traders said rise in crude oil prices, muted opening of domestic equities and foreign fund outflows weighed on the domestic unit.
Meanwhile, brent crude futures, the global oil benchmark, rose 0.42 per cent to USD 67.48 per barrel.
Foreign institutional investors (FIIs) remained net sellers in the capital markets, as they sold shares worth Rs 114.38 crore on Tuesday, as per provisional data.
Domestic bourses opened on a muted note on Thursday with benchmark indices Sensex trading 14.29 points down at 41,446.97 and Nifty lower by 2.85 points at 12,211.70.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was trading unchanged at 97.62.
The 10-year government bond yield was at 6.59 in morning trade. DRR DRR