The gains in the rupee masked a rising sense of caution across markets ahead of the results of elections in several states.
Delhi was the latest to hold assembly elections on Wednesday.
Results will be declared on Sunday with investors watching for clues on how the world's biggest democracy is likely to vote in the general elections due by May.
Any signs that the elections could throw up a divided verdict could disrupt a share rally of nearly 20 per cent since late August.
Investors were also trading carefully ahead of US economic growth data on Thursday and monthly employment data on Friday, which will help set expectations for the
"The rupee is primarily being helped by the Power Grid share inflows, which may be to the tune of $400-$500 million," said Uday Bhatt, a senior manager at UCO Bank.
The gains were largely supported by foreign purchases of the currency from Power Grid Corp of India's $1.1 billion share sale, which was fully covered on the second day of the sale, as per exchange data.
The partially convertible rupee closed at 62.05/06 per dollar compared with 62.36/37 on Tuesday.
It rose 0.5 percent, its biggest single-day percentage gain in a week.
The rupee continued to face a key resistance at breaching 61.9 to the dollar, the top of its late-October trading range.
However, most Asian shares and emerging market currencies fell on fears that the Fed may start scaling back stimulus on the back of recent strong US data.
In the offshore non-deliverable forwards, the one-month contract was at 62.52, while the three-month was at 63.48.
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