The 12 paise was up from its record low on Friday, up to 78.20 against the US dollar, a rebound in crude oil prices.
The foreign exchange opened at 78.20 against the American dollar. The local currency saw a high of 78.19 and a low of 78.24 against the US dollar in initial trade.
The US dollar was at a new all-time low of 78.32 on Thursday.
The dollar index, which measures the strength of the pound against a basket of six currencies, was trading 0.16 per cent lower at 104.26.
The global oil benchmark of Brent crude futures fell 0.21 per cent to USD 109.82 per barrel.
Anil Kumar Bhansali, head of Treasury, Finrex Treasury AdvisorsTreasury Advisors said the rupee opened at 78.20 as the dollar index fell slightly, while Brent remains at USD 110 per barrel levels.
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, according to a range of 78 to 78.40.
On the domestic equity market front, the Sensex was trading 481.95 points or 0.92 per cent higher at 52,747. 67, while the broader NSE Nifty advanced 124.95 points or 0.8 per cent to 15,681. Foreign institutional investors were net sellers in the capital market on Thursday as they offloaded shares worth Rs 2,319. As per stock exchange data, 06 crore were reported.