The rupee weakened by 3 paise to 64.07 against the US dollar in opening trade today on some demand for the American currency from importers and banks.
Forex dealers said a weak dollar in overseas markets and early gains in stock markets capped the rupee losses.
The dollar was trading lower against Japanese yen in Asian trade today.
Yesterday, the rupee had lost 55 paise or nearly 1 per cent -- its biggest single-day crash in eight months -- to end at a fresh two-week low of 64.04 against the US dollar, hit by a double whammy of rising global crude prices and worsening trade deficit.
Meanwhile, the benchmark BSE Sensex recovered by 70.65 points, or 0.20 per cent, to 34,841.70 in early trade today.
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