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The rupee is trading at 60.54/55, off the session low of 60.68 and versus Monday's close of 60.5250/5350.
Traders said gains in the domestic share market are aiding sentiment for the rupee. Nifty is up 0.7%.
Most Asian FX, however, is trading weaker against the dollar, limiting a further fall in the USD/INR pair.
Dollar inflows are also low following the US Labor Day holiday on Monday.
The rupee is seen in a 60.50-60.75 range during the day.
