The rupee resumed higher at 54.68 per dollar against the last closing level of 54.75 at the Interbank Foreign Exchange (Forex) Market.
It moved up further to 54.61 before quoting 54.71 at 1050 hrs.
It moved in a range of 54.61 and 54.75 per dollar in the morning deals.
In New York, the dollar rose for a third day, buoyed by jitters over the potential US economic impact of the so-called fiscal cliff, while the euro came under pressure on last Friday as a result of fading expectations for a near-term decision on a long-delayed tranche of aid for Greece.
Meanwhile, the Indian benchmark 30-share index, Sensex, failed to maintain initial gains and dropped by 33.63 points or 0.18 percent to 18,650.05 at 1100 hrs.