Dealers attributed the rupee fall to dollar gains against other currencies overseas after minutes from the Federal Reserve's October meeting showed policymakers were considering cutting its stimulus programme in coming months.
They said a weak opening in the domestic equity market too put pressure on the rupee.
The rupee had lost 21 paise to close at 62.57 against the dollar yesterday as local stocks declined.
Meanwhile, the BSE benchmark Sensex fell by 161.89 points, or 0.78 per cent, at 20,473.24 in early trade today.