Traders also cited disappointment about the piecemeal approach to providing details after Finance Minister P Chidambaram on Monday unveiled a slew of broad measures to curb imports and attract capital inflows.
The government on Tuesday announced hikes in import duties for gold and silver, but it has yet to unveil other details such as its plan to tax imports of non-essential items.
Meanwhile, the Reserve Bank of India is expected to spell out how banks will be allowed to attract deposits from Indians abroad as also some liberalisation of overseas borrowing rules.
Unless policy makers can provide more details, sentiment will remain cautious, traders said.
"The structural issues like the high current account deficit remains unresolved. Until inflows actually start coming in, which could be over a period of six months, we will continue to see weakness," said N. S. Venkatesh, treasurer at IDBI Bank.
"The near-term weakness will continue and we may see 60.50 to 61.50 range holding for a bit. The market is shallow, there is a genuine demand, so clearly there is downward pressure on the rupee," he added.
The partially convertible rupee closed at 61.43/44 per dollar compared with 61.19/20 on Tuesday. Financial markets will remain closed on Thursday for a national holiday.
India's headline annual inflation rate rose to a five-month high of 5.79 percent in July as oil import costs and food prices were pushed up by a weaker rupee, raising the stakes for policy makers to address the declining currency.
Still for Wednesday, the euro's gains versus the dollar and gains in domestic shares helped offset dollar demand from importers, limiting the falls in the rupee.
The euro rose against the dollar on Wednesday after better-than-expected French and German growth data indicated the euro zone had probably climbed out of a long recession.
Indian shares rose for a fourth consecutive session, led by Tata Group companies after Tata Motors surged on unit Jaguar Land Rover's July sales, while Tata Steel gained as its quarterly profit nearly doubled.
In the offshore non-deliverable forwards, the one-month contract was at 61.99, while the three-month was at 62.93.
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 61.50 with a total traded volume of $2.43 billion.