The rupee lost 13 paise against the dollar to 64.71 in early trade on Thursday on the Interbank Foreign Exchange due to appreciation of the US currency overseas.
Increased demand for the dollar from importers also put pressure on the rupee.
Dealers attributed the rupee's fall to dollar gains against other currencies overseas but a higher opening of the domestic equity market capped the fall.
On April 19, the rupee had gained 5 paise to close at 64.58 a dollar on fresh selling of the American currency by banks and exporters.
Meanwhile, the BSE benchmark Sensex rose 63.57 points, or 0.22 per cent, at 29,400 in early trade on Thursday.