Dealers say good demand for dollars from oil firms seen around 60 levels.
Traders expect the rupee to hold in a 59.90 to 60.20 range during the session, and domestic shares would be watched for cues on foreign fund flows.
The BSE Sensex trading up 0.2 percent.
Asian shares drew a measure of comfort from dovish comments by the U.S. Federal Reserve chief and signs of easing tensions in Ukraine after Russian President Vladimir Putin called on pro-Moscow separatists to postpone a succession vote.
Traders, however, say losses in other Asian currencies and the dollar's gains versus the euro will limit a sharp fall in the USD/INR pair.