Private oil companies buying heard by dealers which pushed the pair to 61.49.
Private bank dealer expects a correction in majors and subsequent weakness in INR.
Traders are now looking to September U.S. payrolls due on Tuesday, with the market forecasting a jobs gain of 180,000, although the data will shed little light on the impact of the policy paralysis in Washington.
The Reserve Bank of India said on Friday its dollar window for oil marketing companies remains open, adding that any tapering would be done in a calibrated manner.
The dollar was mired near an eight-month low against a basket of currencies on Monday on growing expectations the U.S. Federal Reserve will have to delay scaling back its stimulus following a 16-day government shutdown.