Showing weakness for the second day in a row, the rupee depreciated further by 6 paise to quote at 63.96 following sustained dollar selling by exporters on the back of a firm US currency overseas.
Continued capital outflows and cautious local stocks ahead of announcement of macro economic data later in the day also weighed on the rupee, a forex dealer said.
The rupee started weak at 64.05 from its previous close of 63.97 at the Interbank Foreign Exchange (Forex) market. It later moved in a range of 63.96 and 64.05 before trading at 64.02 at 1222 hours, a rise of 0.03%.
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Yesterday, it was down 13 paise, or 0.20%.
The BSE Sensex today was trading at 26,474.74, up 103.76 points, or 0.39%, at 1217 hours after plunging 469.52 points, or 1.75%.
Meanwhile, foreign portfolio investors (FPIs) pulled out Rs 622.89 crore yesterday, according to provisional data.
The dollar index was trading up by 0.07% in Asian trade today against its six major global rivals.