The rupee rose to 59.1900/1950 from its Thursday close of 59.33/34, tracking gains in local equities and Asian currencies' strength against the dollar.
The Sensex and Nifty inched closer to record highs hit on May 16, led by gains in upstream oil and gas companies and due to foreign inflows coming in for a fourth straight day.
Traders expect further gains in the rupee to be capped due to the central bank's dollar buying through state-owned banks.
The pair is seen in a 59.18 to 59.30 range until close.