The dollar sales, however, helped cap further sharp losses, traders said.
The rupee settled at 83.5650 against the U.S. dollar, 0.1% below its close of 83.5050 in the previous session.
The Indian currency has been hovering near its record low of 83.5750 hit in April but regular market intervention from the Reserve Bank of India has curbed the decline, traders said.
Choppy trading last week due to the national election results spurred increased hedging from importers and exporters, data from a local clearing house showed.
Most Asian currencies slipped on Tuesday, with the Korean won, down 0.2%, leading losses. The dollar index was slightly higher at 105.2.
The dollar index will need to close below "gap support" at 104.95 to reverse an otherwise bullish near-term outlook, ING Bank said in a note.
Traders awaited the Federal Reserve's policy decision, due Wednesday, where the central bank is expected to keep rates unchanged. Attention will be on Fed Chair Jerome Powell's remarks and changes to the interest rate dot plot.
The crucial U.S. consumer inflation data is also due on Wednesday. Economists polled by Reuters have forecast that month-on-month core CPI held steady at 0.3% in May.
"Don't think there's a lot of fresh positioning (on USD/INR) currently as people are mostly waiting for Fed and U.S. (inflation) data," a foreign exchange trader at a private bank said.
"State-run banks' offers were present but they were not hammering (USD/INR) lower," the trader said.
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