The rupee was trading weak by 34 paise at 63.37 against the dollar at 4.05 pm local time.
The rupee opened lower by 21 paise at 63.24 against the previous close of 63.03 on the first trading day of the New Year due to buying of American currency by banks and importers.
It hovered in the range of 63.19 and 63.40 in the afternoon trade.
Dealers said increased demand for the American unit from importers and a lower opening in the domestic equity market weighed on the rupee.
Dollar’s gain against major world currencies also influenced the rupee movement, they added.
The rupee had appreciated by 35 paise to end at a two-week high of 63.03 against the greenback yesterday.
Meanwhile, the 30-share BSE index Sensex ended up by 8.12 points or 0.03 per cent at 27,507.54.