Traders will continue to focus on the measures the Narendra Modi-led government will take to bring down the fiscal deficit and fight inflation.
Prime Minister Modi is expected to unveil his top 10 policy priorities on Thursday, seeking to unblock an investment logjam and setting deadlines for action in order to revive the economy.
The market will also focus on the central bank's monetary policy review on June 3, which will be the next key event.
"There was good dollar buying seen from state-run banks in the second half today, most of it related to oil," said Uday Bhatt, a foreign exchange dealer with UCO Bank.
"Next week's policy review will be crucial as the central bank could give its outlook, as also some indication of its expectations from the new government on the inflation and current account deficit front," he added.
The partially convertible rupee closed at 59.03/04 per dollar compared to 58.93/94 on Wednesday.
Indian Oil Corp's total dollar repayment due under the forex swap window to the Reserve Bank of India has been squared off and the final settlement will be on Friday, said P.K. Goyal, the company's director finance, on Thursday.
Dealers said there was some demand seen for the final settlement of these oil swaps in late trade, adding to the rupee's sell-off.
Losses in the domestic sharemarket also hurt sentiment for the rupee as the NSE index posted its biggest daily fall in nearly four months and its third fall over the past four sessions.
In the offshore non-deliverable forwards, the one-month contract was at 59.26 while the three-month was at 59.83.