The rupee's decline was limited by a rally in local stocks, which took the key Sensex index to a new closing high, and continued foreign fund inflows.
It was the second month of gains for the rupee, which rose 1.8 per cent in October after appreciating 4.7 per cent in September. The local currency has recovered since dropping to all-time low of 68.85 on August 28.
Later, it dropped to 61.56 before settling at 61.50, a fall of 27 paise or 0.44 per cent. In the past two days, the rupee had risen 29 paise to the highest level in more than two weeks.
Month-end dollar buying from importers, mainly oil refiners, weighed on the rupee.
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The dollar index was up 0.26 per cent against major global rivals after the Federal Reserve yesterday held its monetary policy steady, in line with expectations.
The 30-share benchmark S&P BSE Sensex rose 130.55 points, or 0.62 per cent, to a record close of 21,164.52. Overseas investors were net buyers of Indian stocks for the 19th straight session, picking up Rs 1,016.77 crore of shares yesterday, according to provisional data with the stock exchanges.