The rupee trimmed its initial gains and was down by 2 paise to 63.72 per dollar in late morning deals on dollar demand from importers on the back of higher dollar overseas.
The rupee resumed steady at yesterday's closing level of 63.70 at the Interbank Foreign Exchange (Forex) market.
However, it failed to maintain initial gains and was quoted at 63.72 per dollar at 1040 hours on bouts of dollar demand. The rupee hovered in a range of 63.75 and 63.66 during the morning deals.
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Meanwhile, the BSE Sensex was trading down 172.32 points, or 0.62%, at 27,676.67 at 1045 hours.