The rupee was up 8 paise at 64.53 against the dollar in opening trade on Friday, helped by stronger domestic equities.
Apart from the selling of the American currency by exporters, forex dealers said, foreign capital inflows and the dollar losing muscle against other currencies overseas kept the rupee in good stead.
The domestic stock market jumped to fresh highs in the beginning.
Investors are relieved that US President Donald Trump has picked Federal Reserve Governor Jerome Powell to lead the US central bank.
Yesterday, the rupee had surrendered early gains and ended marginally lower by 2 paise at 64.61 against the American currency in a quiet session.
The benchmark BSE Sensex rose by 119.36 points to hit an all-time high of 33,692.58 while the NSE Nifty climbed 37.90 points to a new peak of 10,461.70.