Dealers attributed the fall to the dollar's gains after China devalued yuan, which pushed up demand from importers for the US currency.
However, a higher opening in domestic equity market capped losses to some extent.
The rupee had lost six paise to settle at 63.87 against the dollar in yesterday's trade on fag-end demand for the greenback from importers.
Meanwhile, the benchmark BSE Sensex was trading higher by 103.40 points, or 0.36 per cent, at 28,205.12 in early trade today.
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