Still, Indian shares fell after software services exporters such as Tata Consultancy Services retreated from recent highs due to profit-taking.
"The overall dollar weakness helped the rupee and we could see this rally last for some more time. May be a test of 60 is imminent," said Hari Chandramgethen, head of foreign exchange trading at South Indian Bank.
"Medium-term negatives like the Fed taper, elections remain but the market is slowly digesting those facts. I expect 59-60 levels to get supported and good demand will be seen from those levels," he added.
The partially convertible rupee closed at 61.23/24 per dollar compared with 61.8350/8450 on Tuesday. The unit moved in a range of 61.20 to 61.73 during the session.
Financial markets were closed on Wednesday for a local holiday.
In the offshore non-deliverable forwards, the one-month contract was at 61.64, while the three-month was at 62.61.
In the currency futures market, the most-traded near-month dollar/rupee contracts on the National Stock Exchange, the MCX-SX and the United Stock Exchange all closed at around 61.36 with total traded volume at $2.05 billion.