The rupee recovered from initial losses, but was still quoted down by two paise at 63.73 against the dollar in late morning trade on mild demand for the US currency from banks and importers.
The rupee resumed lower at 63.90 as against the previous close of 63.71 at the Interbank Foreign Exchange market.
However, it recovered to 63.69 a dollar before quoting at 63.73 at 1045 hours.
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Meanwhile, the Indian benchmark Sensex recovered 36 points, or 0.18 per cent, to 20,318.37 at 1050 hours.