The domestic unit opened lower at 65.39 as against last Friday's level of 65.27 at the Interbank Foreign Exchange (forex) market and dropped further to 65.62 before ending at one-month low of 65.59, showing a loss of 32 paise or 0.49 per cent.
It hovered in the range of 65.36 and 65.62 during the day's trade.
The local currency had last ended at 65.59 on September 29, 2015.
The US dollar edged down in early Asian trade as investors' appetite for risk dried up against a background of downbeat Chinese factory surveys.
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According to data, China's official manufacturing purchasing managers index remained unchanged at 49.8 in October from what it was a month ago, undershooting the 50.0 level.
Oil prices fell in early Asian trade as analysts expect weaker demand from China in upcoming months.
Meanwhile, the benchmark BSE Sensex ended lower by 97.68 points, or 0.37 per cent, at 26,559.15.