This is the third straight slide, which dealers say is mostly due to incoming demand for the US currency and a lower opening in the domestic stock market.
But the continuing political turmoil surrounding US President Donald Trump's recent executive decisions and uncertainty about his economic agenda put the dollar in a spot of bother overseas, which somewhat limited the rupee's slump.
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Yesterday, the rupee had ended lower by 7 paise at 64.15 due to sustained demand for the greenback from importers.
Stocks, in the meantime, got off to a decisively weak start as the benchmark Sensex retreated from record highs by falling 222.21 points, or 0.72 per cent, at 30,436.56 in the early session.