"We expect the market to remain volatile ahead of the key events lying in the month of November which include India's IIP and inflation data followed by GDP at the month end."
Meanwhile, the premium for the forward dollar closed sharply lower on fresh receipts by exporters.
The benchmark six-month forward dollar premium payable in April settled down at 154-156 paise from yesterday's close of 161-163 paise.
Far-forward contracts maturing in October also reacted downwards to 292-1/2-294-1/2 paise from 299-301 paise.
The RBI has fixed the reference rate for the US dollar at 54.4403 and for euro at 69.4755.
The rupee also fell back slightly against the pound sterling to 86.73 from Wednesday's close of 86.67. It dipped against the Japanese yen to 68.09 per 100 yen from 67.54.
Rupee, however, remained firm against the euro to 69.28 from last close of 69.48.
Meanwhile, FIIs pumped in USD 137.29 millio yesterday as per Sebi data.