The rupee opened 12 paise up from its record low against the US dollar on Friday, tracking a pullback in crude oil prices.
The rupee opened against the American dollar at 78.20 at the interbank foreign exchange. In initial trade, the local currency had a high of 78.19 and a low of 78.24 against the US dollar.
The rupee had closed at its all-time low of 78.32 against the US dollar on Thursday.
The dollar index, which gauges the strength of the dollar against a basket of six currencies, was trading 0.16 percent lower at 104.26.
The rupee opened at 78.20 as the dollar index fell slightly, while Brent remains at $110 per barrel, according to Anil Kumar Bhansali, head of Treasury, Finrex Treasury AdvisorsTreasury Advisors.
Foreign portfolio investors FPI continue to buy US dollar, along with oil companies, while the Reserve Bank of India continues to sell and protect the rupee, Bhansali said.
On the domestic equity market, the 30 share Sensex was trading 481.95 points or 0.92 percent higher at 52,747. The broader NSE Nifty increased by 124.95 points or 0.8 percent to 15,681. Foreign institutional investors offloaded shares worth Rs 2,319. They remained net sellers in the capital market on Thursday. According to stock exchange data, 06 crore were reported.