On Monday in early trade, the rupee went down by 9 paise to 64.79 against the US dollar at the interbank foreign exchange amid fresh foreign fund outflows.
The rupee's fall has been attributed by dealers to an increased demand for the US dollar from importers and banks and a lower opening in the domestic equity market.
On Friday, the rupee had lost 12 paise to close lower at 64.70 a dollar due to renewed demand for the US currency.
Foreign investors pulled out Rs 416.28 crore from equity markets on Friday, as per provisional data.
Standard & Poor's on Friday kept its sovereign rating for India unchanged at 'BBB-minus' with 'stable' outlook saying vulnerabilities stemming from low per capita income and high government debt balance strong GDP growth.
Meanwhile, the benchmark Sensex fell by 106.92 points, or 0.31 per cent, to 33,572.32 in early trade.
(With PTI inputs)