The rupee resumed lower at 63.72 as against Monday's closing level of 63.67 at the Interbank Foreign Exchange (Forex) market.
Later, it fell sharply to 63.77 per dollar, and was quoting at 63.75 per dollar at 1030 hours. It moved in a range of 63.72-63.77 per dollar during morning trade.
In New York, the US dollar ruled higher against its major rivals in early trade and hovered near a 29-month high against the euro after a Greek vote triggered the dissolution of the country's parliament and anxiety about potential trouble ahead for financial markets.
Meanwhile, the BSE 30-stock index, Sensex, was trading almost flat, marginally up by 1.92 points, or 0.01 percent to 27,397.65 in late morning trade.

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