The rupee is trading at 61.52/53 after hitting 61.49, its highest since December 12. It had closed at 61.89/90 on Friday.
Gains in the domestic sharemarket and broad losses in the dollar are helping the rupee but demand for the greenback from oil companies is limiting further gains.
Surprise contraction in the factory output in November is also hurting sentiment for the pair.
The consumer price inflation data due to be released at 5:30 pm (1200 GMT) will be crucial for further near-term direction.
The BSE Sensex is up 1.3%.