Increased month-end dollar demand from importers also put pressure on the rupee.
Dealers attributed the rupee's fall to dollar gains against the euro overseas and cautiousness ahead of the RBI monetary policy review today but a higher opening in the domestic stock market, restricted the fall.
The rupee had lost 37 paise, the most in a week, to close at Rs 59.41 yesterday against the dollar.
Meanwhile, the BSE benchmark Sensex rose by 27.31 points, or 0.13 per cent, at 19,620.57 in early trade today.