Investors are cautious ahead of consumer price inflation data due later in the day.
Moreover, the US dollar's gains against some currencies overseas, on surging crude oil prices and growing geopolitical uncertainties, weighed on the domestic unit, forex dealers said.
However, a higher opening of the domestic equity market capped the rupee's fall.
The benchmark BSE Sensex regained 34k level rose by 62.38 points, or 0.18 per cent, to 34,002.82 in the opening trade.
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