Reuters Market Eye - The rupee is not far from its record low of 58.98 hit last week, trading at 58.45 versus 57.87/88 at Monday's local close.
A large private corporate USD seller is capping gains for the pair, say several dealers.
BSE Sensex down 0.23 percent.
USD/INR NDFs surge overnight, closing NY trade at 58.56-58.59.
The local currency may find some comfort from RBI's concerns about the impact of the falling rupee on imported inflation.
The U.S. dollar hovered above a two-month low against the yen on Tuesday but uncertainty ahead of the outcome of the U.S. Federal Reserve meeting is likely to cap further gains.
(Reporting by Subhadip Sircar)