However, good dollar inflows prevented the unit from sliding sharply despite domestic stocks falling by nearly 1%.
Foreign funds have bought shares worth $2.3 billion and debt worth $2.90 billion so far in June, taking total inflows in the year to $9.9 billion and $10.5 billion, respectively.
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Some residual dollar inflows related to Reliance Communications' share sale could have come in, dealers said.
Reliance Communications Ltd on Wednesday raised $804 million by selling shares in what is the single biggest equity issue since the pro-business Narendra Modi government took office.
The Indian rupee ended at 60.14/60.15 to the dollar after trading in a narrow 60.08-60.20 band compared with Wednesday's close of 60.1250/1350.
Brent crude dropped under $114 a barrel on Thursday as most of Iraq's oil output remained unaffected by the militant insurgency in the country, although worries over the conflict kept a floor under prices.
However, Asian currencies were up with South Korean won leading the gains as a disappointing contraction in the U.S. economy during the first quarter raised expectations that the Federal Reserve may not hurry to increase interest rates.
Indian shares ended lower, led by fall in oil explorers after the government deferred a decision to hike prices of locally produced gas, while the expiry of monthly derivatives contracts also weighed on sentiment.
In the offshore non-deliverable forwards, the one-month contract was at 60.40, while the three-month was at 60.98.
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