This was on hopes of more foreign capital inflows into equity market amid exit polls predicting a strong showing by the BJP in the recently concluded Assembly elections to four states.
The rupee resumed higher at 61.75 as against the last closing level of 62.05 per dollar at the Interbank Foreign Exchange (Forex) Market and firmed up further to a one-month high of 61.53 before quoting at 61.59 per dollar at 1045hrs.
It hovered in a range of 61.53-61.86 per dollar during the late morning trade.
In New York market, the U.S. dollar surrendered some of the gains scored after a report on private-sector payrolls underlined ideas the Federal Reserve could move sooner than previously thought to cut back on its monthly bond purchases.
The Indian benchmark sensex rose by 369.87 points or 1.79 per cent to 21,078.58 at 1045hrs.