Firm local equities, fresh capital inflows and some weakness in dollar overseas restricted the rupee fall to some extent, a forex dealer said.
At the Interbank Foreign Exchange (Forex) market, the domestic unit commenced lower at 63.66 a dollar from last Friday's close of 63.57.
Rupee was later trapped in a narrow range of 63.62 and 63.71 before concluding at 63.67, a fall of 10 paise or 0.16 percent. This is the weakest close since 63.71 on November 12, 2013.
The Indian benchmark S&P BSE Sensex today shot up by 154 points, or 0.57 per cent. FPIs had bought shares worth USD 65.87 million last Friday, as per Sebi data.
The dollar index was down by 0.05 per cent against a basket of six major global rivals.
Pramit Brahmbhatt, Veracity Group CEO said, "Indian rupee started the last week of the year on weaker note and depreciated by ten paise for the day, due to dollar demand from oil companies which dented the Rupee movement."
"Local equities closed on a positive note which capped the rupee losses. The trading range for the spot rupee is expected to be within 63.20 to 64.00," he added.