Besides, strength in the US dollar against some other currencies overseas also weighed on the domestic currency.
Dealers attributed the rupee's fall to increased demand for the US currency and a lower opening in the domestic equity market.
Yesterday, the rupee had shed 3 paise to close at 64.18 against the US dollar on fresh demand for the dollar.
Meanwhile, the benchmark BSE Sensex fell 133.04 points, or 0.44 per cent, to 29,993.17 in early trade today.
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