Besides, a higher opening in the domestic equity market also supported the domestic unit, forex dealers said.
However, the dollar's strength against some currencies overseas capped the rupee's gains.
On Friday, the rupee had staged a resounding comeback to close higher by a whopping 24 paise at 66.61 on fresh dollar unwinding from banks and exporters.
Meanwhile, the benchmark BSE Sensex rose 160.79 points, or 0.57 per cent, to 28,026.75 in early trade.