The rupee opened at 95.72 and touched 95.63, up 11 paise from the previous close of 95.74.
Traders said a cautious RBI stance on inflation could support debt inflows and help the rupee move toward 95.00-95.20.
Sensex and Nifty opened higher, while FIIs sold equities worth ₹4,447.06 crore on Thursday.