The unit, however, dropped on the week, posting its third straight weekly fall, as investors pared positions amid the ongoing national elections.
Foreign funds sold Indian shares worth 446.9 million rupees ($7.4 million) on Wednesday, provisional exchange data showed, marking the third consecutive session of outflows.
"There was good buying from oil firms during the day today. In late trade there was good selling seen from state-run banks," said Vikas Babu Chittiprolu, a senior foreign exchange dealer with the state-run Andhra Bank.
"There are absolutely no triggers to watch out for so the range of 60.00 to 60.60 should continue to hold next week," he added.
The partially convertible rupee closed at 60.29/30 per dollar compared with 60.37/38 on Wednesday. On the week, the rupee fell 0.2 percent, in its third straight weekly drop.
Earlier in the day, the rupee fell to a session low of 60.50 as importers, particularly oil firms rushed to buy dollars in a holiday-shortened week.
Shares rose 1.6 percent, to snap a three-day losing streak as lenders such as ICICI Bank surged on value buying, earnings expectations and hopes of gains in bond portfolios after the central bank's biggest debt auction.
Most emerging Asian currencies too edged up on Thursday as the dollar eased broadly after U.S. Federal Reserve Chair Janet Yellen's dovish comments on monetary policy, while trading was subdued ahead of a holiday in some markets.
In the offshore non-deliverable forwards, the one-month contract was at 60.76 while the three-month was at 61.53.