The rupee resumed higher at 62.30 per dollar as against the last closing level of 62.37 at the Interbank Foreign Exchange (Forex) Market and firmed up further to 62.28 per dollar.
However, it trimmed its initial gains and was quoted at 62.35 per dollar at 1045 hours.
It moved in a range of 62.28 and 62.38 per dollar during the morning deals.
In New York market, the dollar rose to its highest level yesterday against the yen in February, while the euro strengthened after the region's top central bank dismissed the threat of deflation in the euro zone, prompting questions about future easing actions.
Meanwhile, the benchmark BSE Sensex rose by 75.06 points, or 0.37 per cent, to 20,385.80 at 1045 hours.