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Foreign funds have bought a total of $3.3 billion in debt and equities so far in December. Shares edged up as blue-chips extended a rally, although bonds fell for a fourth consecutive session.
Trading was thin because of the holiday week, with major financial centers such as London also closed on Thursday.
"The market has been very dull. There will be month-end demand continuing while we could also see some year-end dollar selling which will keep the unit in a range," said Hari Chandramgethen, head of foreign exchange trading at South Indian Bank.
Chandramgethen predicted a 61.65 to 62.15 per dollar range for Friday.
The partially convertible rupee closed at 62.16/17 per dollar compared to 61.79/80 on Tuesday. Financial markets were closed on Wednesday for Christmas.
Oil firms tend to buy more dollars towards the end of each month to pay their import bills, an impact that can be magnified on days of thin volumes.
In the offshore non-deliverable forwards, the one-month contract was at 62.59 while the three-month was at 63.41.
(Editing by Sunil Nair)
