The rupee depreciated 10 paise to 64.38 against the US dollar in opening trade on Thursday due to increased demand for the US currency from importers amid fresh foreign funds outflow.
However, a weak dollar in global markets helped the rupee limit its losses, dealers said.
The rupee opened weak at 64.38 at the interbank forex market against its previous close of 64.28.
The rupee moved in range of 64.29 to 64.38 in early deals before trading at 64.33, down by 5 paise, at 0930hrs.
Foreign investors pulled out a net Rs 1,022.50 crore from stocks on Wednesday.
On Wednesday, the rupee had lost 4 paise versus the dollar to end at 64.28 after RBI sounded a more hawkish tone amid upside risks on inflation.
Meanwhile, the benchmark Sensex rose 167.73 points, or 0.49 per cent, to 34,250.44 in early trade.