Traders said the market would continue to remain rangebound in the absence of any major clues in the near-term.
The key retail and wholesale price inflation data is due to be released only next week, keeping markets in a tight range this week, they added.
"There were good inflows seen today, a large engineering firm was also selling. No major events this week, so expect a range of 61.20 to 61.80 on the pair," said Hari Chandramgethen, head of foreign exchange trading at South Indian Bank.
The partially convertible rupee closed at 61.43/44 per dollar compared with 61.61/62 on Wednesday. The rupee earlier rose as high as 61.3025, its strongest level
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