The partially convertible Indian currency finished at the day's low of 51.72 to the dollar after being as high as 51.34.
The rupee closed lower versus the US dollar on Wednesday as importers bought the greenback ahead of the EU Summit where European leaders are set to announce a comprehensive package to resole the region's debt crisis.
The partially convertible Indian currency finished at the day's low of 51.72 to the dollar after being as high as 51.34. It had opened at 51.35 as against Monday's close of 51.42.
Indian markets were shut on Tuesday for a public holiday.
Meanwhile, the euro fell against the dollar and the yen, reversing earlier gains, after a German government official was quoted as saying that the nation would reject proposal to combine current and permanent euro-area rescue funds.
The Dollar Index rose for the first time in three days.
The Australian dollar rose after a report showed that third-quarter gross domestic product (GDP) grew faster than economists' forecast.