Expectations of FII inflows into Rs 20,000 crore FPO of Adani Enterprises also bolstered the local currency.
At the interbank foreign exchange market, the rupee opened higher at 81.51 against the previous close of 81.61 on Wednesday.
The money markets were closed on Thursday for the Republic Day holiday.
The rupee moved in a range of 81.50 to 81.58 in early trade. It was trading at 81.52 to a dollar at 0940 hours.
Meanwhile, the US dollar index, which gauges the greenback’s strength against a basket of six currencies, edged up 0.08 per cent to 101.92.
Brent crude was trading 0.34 per cent higher at USD 87.77 per barrel.
The Joint Ministerial Monitoring Committee of OPEC will meet next week to take a call on the output and full meeting of the cartel and allies.
Also, the 20,000 crore FPO of Adani Enterprises opened on Friday. The company raised around Rs 6,000 crore from anchor investors.
On the domestic equity market front, the 30-share BSE Sensex declined by 578.19 points to 59,626.87 while the broader Nifty fell 144.7 points to 17,747.25 in early trade.
Foreign Institutional Investors (FIIs) were net sellers in the capital market on Wednesday as they sold shares worth Rs 2,393.94 crore, according to exchange data.