The rupee is trading at a session high of 62.8050/8150, higher than its close of 63.10/11 on Monday.
Traders say some corporate dollar sales are helping the rupee while the RBI's dovish policy statement is also aiding the sentiment.
They expect the pair to hold in a 62.75 to 63.15 range during the rest of the session.
The RBI unexpectedly raised rates by 25 basis points earlier in the day, but said if consumer price inflation eases as projected it does not foresee any near-term tightening.
The central bank governor said in a post-policy press conference that once inflation comes down to comfortable levels, the RBI would have some room to cut rates.
Traders will continue to monitor foreign fund flows into and out of the local debt and equity markets for direction. The BSE Sensex trading down 0.2 percent.