Foreign portfolio investors sold shares worth a net Rs 826.77 crore, provisional data of stocks exchanges showed.
The domestic currency started on a negative note at 64.17 against the Wednesday's closing level of 64 at the forex market before concluding at 64.12 a dollar, a loss of 12 paise or 0.19 per cent.
The rupee had ended 4 paise higher yesterday.
Meanwhile, the Reserve Bank fixed the reference rate for the US dollar at 64.0692 and for the euro at 76.1398.
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On the domestic bourses, the BSE benchmark Sensex moved up by 55.52 points, or 0.17 per cent, to close at 32,241.93, while the NSE Nifty rose marginally by 7 points.
The dollar index, which measures the greenback's value against a basket of 6 global currencies, dropped by 0.09 per cent in the late afternoon trade.
The American unit consolidated its gains today, a day after posting its biggest single-day rise in six weeks as markets looked forward to US inflation data which will determine the near-term outlook for the struggling dollar.
In cross-currency trades, the rupee ended lower against the pound sterling at 85.40 per pound as against the previous closing of 84.94 but rose against the euro to end at 76.18 from 76.69.
The domestic unit firmed up further against the Japanese yen to settle at 57.96 per 100 yens from 58.16 per yesterday.
In forward market today, the premium for dollar eased further on sustained receivings from exporters.
The benchmark six-month premium payable in February eased further to 121.75-123.75 paise from 125-127 paise yeterday, while the far-forward August 2018 contract also fell to 262- 264 paise from 266-268 paise.