The Indian unit opened sharply higher at 64.80 as against Wednesday's closing level of 65.12 at the Interbank Foreign Exchange (forex) market.
Forex market was closed yesterday for the 'Dussehra' festival.
It hovered in the range of 64.89 to 64.77 during the morning deals before quoting 64.88 at 1030 hrs.
"Looking at positive global cues, the rupee is expected to appreciate though the strength in dollar may put some pressure," a forex dealer said.
"Will see the range for today between 64.75-65.60 per dollar." he further added.
The dollar index is currently trading down by 0.09% at 96.32 as against a basket of six currencies.
Globally, the euro fell to its lowest level in two months yesterday after European Central Bank President Mario Draghi all but promised the central bank would expand its program of quantitative easing at its December meeting.
Meanwhile, the benchmark BSE Sensex was trading higher by 219.48 points, or 0.80%, at 27,507.14 at 1035-hrs.
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