The domestic unit resumed higher at 60.87 per dollar as against the last closing level of 60.95 at the Interbank Foreign Exchange (Forex) Market.
It gained sharply to 60.84 on sustained bouts of dollar selling, before quoting at 60.91 per dollar at 1025 hrs.
The rupee was hovering in a range of 60.93 and 60.84 per dollar in late morning deals.
Crude oil prices were trading higher in Asia today after US President Barack Obama vowed to destroy jihadist militants in crude producers Syria and Iraq, though weak global demand and a supply glut capped gains.
Meanwhile, the benchmark BSE Sensex was trading higher by 27 points or 0.10 per cent at 27,084.44 at 1030 hours.