Dealers attributed the rupee's fall to dollar gains against the euro overseas and sustained demand for the American currency from importers.
The rupee had closed 8 paise lower at 54.69 a dollar in yesterday's trade on heavy demand for the American currency.
Meanwhile, the BSE benchmark Sensex was down by 34.22 points, or 0.17 per cent, at 19,783.41 in early trade today.