Foreign institutional flows continue to hurt the pair. Overseas investors bought Indian shares worth $142.8 million on Tuesday, provisional exchange data shows. The BSE Sensex is trading up 0.65 percent.
USD/INR is seen trading in a range of 59.90 to 60.10 during the session, dealers say.
Most Asian currencies trading stronger against the dollar.
Traders expect the RBI to step up dollar purchases should foreign fund inflows continue through the day.
The RBI bought a net $14.51 billion in the forward market in May compared with net forward dollar sales of $6.09 billion in April, according to Reuters calculations based on data available on the RBI's website.