Traders expect the rupee to remain wedged between the 59.60 and 60.50 levels in the absence of any key triggers in the near-term.
The next major event for the financial market is the RBIs monetary policy review on August 5.
The NSE index rose to a record high, gaining for a seventh straight session.
The rupee closed at 60.0925/1025 compared with 60.24/25 on Tuesday. The unit hit 60.0550 during the session strongest since July 14. Traders will continue to monitor moves in other Asian currencies for clues in the near-term. Most Asian currencies gained. But dealers say oil-related dollar demand, which is due to gather pace towards the month-end, is likely to cap broader gains in the rupee, while a stand-off between Russia and the West also continues to spark uncertainty.