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The rupee rose from a session low of 60.2450 to trade at 60.09/60.10, as gains in shares helped offset dollar demand from state-run banks. It closed at 60.07/60.08 on Monday.
State-run banks have been mopping up dollars for oil- and defence-related payments in the recent sessions, aiding the greenback.
Some of this demand could be for the government's effort to pay Iran a part of its oil dues, dealers say.
The Nifty is up 0.3%, heading for its first daily rise in six sessions as interest rate-sensitive stocks gained after June consumer inflation slowed to the lowest since figures were first published in January 2012.
