Dealers said early losses in domestic equity markets and increased foreign fund outflows weighed on the rupee.
The dollar, however, was trading weak against Asian currencies after its overnight losses against the euro and the pound which capped its losses.
The rupee moved in a range of 64.33 to 64.40 in early trade.
Yesterday, the rupee had closed marginally up 2 paise at 64.26 against the US dollar in line with a good recovery in equity markets.
Foreign investors sold shares worth Rs 2,297 crore on net basis yesterday.
The benchmark BSE Sensex crashed 563.51 points, or 1.63 per cent, to 33,849.65, while Nifty tanked by 178.65 points, or 1.68 per cent, to 10,398.20 in opening trade.
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