The sharp fall in the euro following the stimulus talks however weighed on rupee sentiment, dealers said.
Traders expect currency markets to remain cautious ahead of the Reserve Bank of India's policy review on Dec. 2. The central bank is expected to adopt a more dovish tone but is seen as unlikely to cut interest rates until February.
India is also due to report July-September economic growth data on Friday, adding to the caution.
"There was very good demand for dollars from state-run banks which hurt the rupee today," said Hari Chandramgethen, head of foreign exchange trading at South Indian Bank, predicting a range of 61.50 to 62.50 for the rest of the week.
The partially convertible rupee closed at 61.9350/9450 per dollar compared to 61.7625/7725 on Friday.
The fall came even as domestic shares hit a record high after China unexpectedly cut rates and as prospects of further stimulus in China and Europe whetted risk appetite globally.
Prospect of further reforms at the start of the winter session of parliament on Monday could also prevent much further depreciation in the rupee, traders said, especially as the RBI is seen intervening to keep the rupee from dipping too much below 62 per dollar.
In the offshore non-deliverable forwards, the one-month contract was at 62.20 while the three-month was at 62.74.
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