Firm dollar overseas also weighed on the rupee while rally in local equities capped the fall to some extent, a dealer said.
At the Interbank Foreign Exchange (Forex) market, the domestic unit opened higher at 52.45/46 a dollar from last weekend's close of 52.54/55 and immediately touched a high of 52.43 on firm local stocks.
However, month-end dollar demand from importers, mainly oil refiners, put pressure on the rupee and it fell back to a low of 52.75.
It closed at 52.73/74, a fall of 0.36 per cent. Previously, it had settled at 52.98/99 on January 5, 2012.
Foreign Institutional Investors (FIIs) pulled out a total USD 377.36 mln in first five days of the last week.
FIIs invested a total Rs 479.53 crore in equities today, as per provisional BSE data.
The dollar index was up by over 0.15 per cent against a basket of currencies, recovering after fall on last Friday on softer-than-expected gross domestic product data.
