Increased demand for the American currency from importers and banks meant there was sustained foreign capital outflows.
The dollar's weakness against some currencies overseas, however, kept the fall to a minimum.
Yesterday, the rupee had ended marginally lower by 6 paise to 64.49 against the US dollar in a range-bound trade on fresh bouts of demand for the greenback amid caution among investors ahead of GST rollout from July 1.
The benchmark BSE Sensex fell 62.55 points, or 0.19 per cent, to 31,234.98 in early trade today.
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