The partly convertible rupee finished at 45.80/81 per dollar, off an early session peak of 45.68 and marginally weaker than Tuesday's 45.78/79 close.
The unit hit an intra-day low of 45.86 per dollar but recovered later on investment inflows into the stock market.
"It was a total two-way volatile movement today. There are stock market-related inflows, but oil companies are there to buy at every (dollar) dip and that is keeping the rupee from not firming too much," said a dealer at a private bank.
Finance Minister Palaniappan Chidambaram told reporters on Wednesday the rupee had appreciated against the euro, yen and sterling over the past few months and depreciated only nominally against the dollar.
"It (the rupee) has moved both ways. As we have always said, orderly movement both ways is acceptable. It is only disorderly movement that should cause a concern," he said.
The Reserve Bank of India's deputy governor, Rakesh Mohan, echoed Chidambaram's words and said the rupee's movement has not been volatile.
Traders said the comments indicated authorities were not concerned about the recent depreciation of the rupee against the dollar.
The rupee hit a 13-month intra-day low of 46.06 on Tuesday before suspected central bank intervention sparked an unwinding of long dollar positions by traders that, along with good capital inflows, helped the rupee recover.
Capital market data showed foreign funds, who had been net sellers of more than $800 million worth of local stocks in October, have revived purchases this month and have pumped more than $300 million into Indian equities.