The rupee is trading at 63.26/27 versus Friday's close of 63.2950/3050.
Volumes are thin in the holiday-shortened Christmas week.
The pair is seen in a 63.10 to 63.60 range during the day.
Gains in local shares are helping the Indian unit.
The Nifty is trading up 0.4%.
Month-end demand from importers is expected to weigh.