The spot rupee ended at 158.00/10 per dollar, compared with Monday's close of 157.85/95.
"There was some demand and exporters were silent," a currency dealer said.
Dealers said the rupee could come under pressure with low supply of dollars as tea exporters would stay away due to rains.
Heavy monsoon rains have killed eight people, prompting authorities to warn against landslides and floods in low-lying areas after spill gates had to be opened across the Indian Ocean island.
The rupee hit a record low for a third straight session on May 16 and touched 158.50 per dollar after the central bank chief said on May 11 that the currency would depreciate gradually as dollar outflows surpass inflows.
The currency has declined 0.13 percent so far this month after a 1.5 percent fall in April. It has fallen 2.9 percent this year.
The pressure on the currency is unwarranted as the gross external reserves are at $9.1 billion and the real effective exchange rate indexes indicate that the currency is competitive, the central bank said on Wednesday.
The central bank is "studying carefully" if there was extra pressure on the currency than what was expected, and also the behaviour of market participants, central bank chief Indrajit Coomarswamy had said on May 11.
Dealers said they expect the rupee to gradually weaken and face higher volatility this year due to debt repayments by the government.
Senior central bank Deputy Governor Nandalal Weerasinghe had said early this month that debt repayments by the government will not have an impact on the currency as they are managed with borrowed money externally.
Foreign investors sold government securities worth a net 5.97 billion rupees ($37.86 million) in the week ended May 16, bringing the outflow so far this year to 15.8 billion rupees, central bank data showed.