Dealers said fresh selling of the greenback by exporters and banks and the dollar's weakness against other currencies overseas supported the rupee.
Stock markets opening with gains also backed the rupee, they added.
Yesterday, the rupee had fallen by 11 paise to 64.04 a dollar on persistent demand for the American currency from banks and importers.
Meanwhile, the benchmark BSE Sensex rose by 57.08 points, or 0.17 per cent, at 32,215.74 in early session.
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