The rupee opened a higher at 63.73 per dollar as against yesterday's closing level of 63.78 at the inter-bank foreign exchange here.
It strengthened further to 63.61 per dollar before quoting at 63.65 per dollar at 1100 hrs.
The Indian unit hovered between 63.76 and 63.61 during morning trade.
"Weakness in dollar overseas and sustained FII inflows lifted the rupee," a dealer said.
Foreign investors have put in more than Rs 8,200 crore in debt and equity markets in the past five trading sessions.
The 30-share BSE Sensex was trading flat, marginally up 1.52 points or 0.00 per cent at 36,141.50 at 1040 hrs.