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The rupee is trading at 60.49/50 after hitting 60.47, its highest since August 12 and above its close of 60.77/78 on Monday as dollar selling by custodian banks continued to help.
Foreign funds bought shares worth $241.56 million on Monday, provisional stock exchange data showed.
Stocks though marginally down on the day, continue to remain close to record highs hit on Monday with dollar inflows continuing, dealers said.
Traders expect good support for the pair close to the 60.50 mark. If 60.50 is broken convincingly, the pair can go as low as 60.10, they added.
Dollar demand from importers, particularly oil firms, are limiting the downside, they added.
The dollar held steady against a basket of major currencies on Tuesday, keeping a low profile after slipping on the previous day in the wake of a disappointing reading on US manufacturing activity.
