The rupee, which closed at 55.65 on Monday, resumed higher at 55.39 a dollar at the Interbank Foreign Exchange market.
Thereafter, it touched a high of 55.25 on dollar selling by exporters and initial firmness in local stocks.
The rupee reversed its gains and fell back to the day's low of 55.91, after being hit by heavy dollar demand from importers, mainly oil refiners, on lower oil prices.
It finally closed at 55.64 a dollar after recovering some lost ground.
"Today was a normal trading day without any significant movement.
However, the currency is showing bias towards weakness," T S Srinivasan, GM (Treasury), Indian Overseas
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