However, foreign capital inflows into equity market restricted the rupee's fall to some extent, a forex dealer said.
The domestic currency opened and closed at the same level of 63.64 per dollar at the Interbank Foreign Exchange as compared to yesterday's close at 63.62, showing a loss of two paise.
The rupee has dropped by 12 paise or 0.19 per cent in the last four days.
The dollar index was trading slightly lower against its major global rivals today.
In New York market, the dollar weakened slightly against most of its rivals yesterday, but remained on track to finish the week with modest gains.
Meanwhile, the benchmark Sensex ended lower by 84.13 points to close at 27,811.84 on selling pressure from operators due to fall in global markets as high-level talks between Greek and European officials failed to break a long-standing stalemate over an economic reform plan for Greece.
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