The American currency overseas rose amid fresh foreign funds outflows.
Dealers also attributed the rupee’s fall to increased demand for the US currency from importers and banks.
However, a higher opening in the domestic equity market capped the losses.
On Friday, the rupee had ended down 22 paise to end at a fresh one-month low of 65.16 against the US dollar due to frantic demand for the American unit from importers and corporates.
Foreign investors had pulled out around Rs 529 crore from equity markets on Friday.
Meanwhile, the benchmark Sensex rose 102.74 points, or 0.30 per cent, to 33,417.30 in early trade.
The rupee lost 20 paise to 65.36 against the dollar on Monday on fears that the tax rate decision of the GST Council will have a revenue implication of Rs 20,000 crore annually.