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Traders said the global risk aversion could accelerate foreign fund withdrawals from domestic stocks, which are one of the world's performers this year.
At 9:02 a.m. (0332 GMT), the rupee was at 53.37/38 to the dollar, 0.6 percent weaker than Wednesday's close of 53.07/08.
The euro slid to a 10-year low against the yen and the lowest in nearly a year versus the dollar on Thursday, having suffered a sudden drop the previous day as moves were amplified in poor year-end liquidity.