At the Interbank Foreign Exchange market, the domestic unit commenced better at 62.77 a dollar from last close of 62.81.
It then moved in a range of 62.67 and 62.78 before finishing at 62.70 per dollar, showing a gain of 11 paise or 0.18 per cent.
The rupee has gained by 27 paise or 0.43 per cent in the two days.
Veracity Group chief executive officer Pramit Brahmbhatt said: "Rupee traded strong for the day.
“Exporters and banks were seen selling dollars which supported rupee. . . . Also, local equities traded strong which helped the rupee movement."
The trading range for the spot USD/INR pair is expected to be within 62.35 to 63.15, he added.
In London, the dollar was almost flat against the yen on Tuesday ahead of a closely monitored Federal Open Market Committee meeting in the US.
The dollar rally paused overseas after possibility that weaker-than-expected US data will prompt the Federal Reserve to adopt a cautious stance.
Outcome of the policy meeting will be released on Wednesday.
According to data, manufacturing struggled in February, holding back overall industrial production that rose by a mere 0.1 per cent in the month.
Reports on homebuilder sentiment and regional manufacturing also were weaker than expected.
The dollar index, a gauge of six major global rivals, was down by 0.08 per cent on Tuesday.
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