Moreover, the US dollar's gains against some currencies overseas on strong jobs data put the rupee on backfoot, forex dealers said.
However, a higher opening of the domestic equity market capped the rupee's losses.
The rupee had strengthened by 11 paise to end at a fresh two-year high of 63.58 against the US currency on Friday even as panic dollar unwinding continued.
Meanwhile, the benchmark BSE Sensex rose further by 61.11 points, or 0.18 per cent, to 32,386.52 in early trade.