Brokers said a weak trend in euro in overseas markets also dampened the rupee sentiment against the US dollar.
At the Interbank Foreign Exchange (Forex) market, the domestic currency commenced higher at 54.30 a dollar from overnight close of 54.36. It immediately touched a high of 54.27 on initial jump in local stocks.
However, the weakness in domestic equities after morning session and a sudden gust of dollar demand from importers and some banks dampened the rupee sentiment.
FIIs pulled out USD 37 million (Rs 204 crore) from stocks as per provisional data, putting the rupee under more pressure. The rupee fell back to a low of 54.78, before closing slightly better at 54.75 -- a fall of 39 paise or 0.72 per cent.
This is the lowest closing level for the unit since sending at 55.43 on September 13.
Yesterday, rupee had lost 16 paise or 0.30 per cent, thereby losing 55 paise in two sessions.
The Indian stock market benchmark Sensex surrendered early gains to close sharply lower by nearly 163 points.
"The weakness in the Indian unit was due to weak Euro throughout the day. The Euro was pressurised by the Greece austerity concerns and Spain's delay in seeking a bailout. The gains in the dollar index led by better-than-expected data from the US, also made the rupee fall," said Abhishek Goenka, Founder and CEO, India Forex Advisors said.
Dealers said forex trading was tepid ahead of Diwali holidays with currency markets slated to remain closed on November 13-14.
Meanwhile, the premium for the forward dollar softened further on sustained receipts by exporters.
The benchmark six-month forward dollar premium payable in April eased to 153-155 paise from Thursday's close of 154-156 paise.
Far-forward contracts maturing in October also ended a tad lower at 292-294 paise from 292-1/2-294-1/2 paise.
The RBI has fixed the reference rate for the US dollar at 54.3400 and for euro at 69.4274.
The rupee remained weak against the pound sterling to end at 87.33 from overnight close of 86.73 and also dipped further against the Japanese yen to 69.09 per 100 yen from 68.09.
The rupee, however, fell back against the euro to 69.61 from last close of 69.28.
Meanwhile, FIIs injected USD 56.49 million yesterday as per Sebi data.