However, smart rise in local equities amid sustained capital inflows tried to restrict the fall, a dealer said.
At the Interbank Foreign Exchange (Forex) market, the domestic currency commenced slightly lower at 62.33 per dollar from last weekend's close of 62.31 and immediately touched a high of 62.32.
Later, it met with strong resistance and fell back to a low of 62.5650 before concluding at 62.51, exhibiting a fall of 20 paise or 0.32 per cent.
The dollar index, a gauge of six major global rivals, was up by 0.58 per cent today.
The benchmark BSE Sensex today bounced by 165.06 points or 0.57 per cent to cross 29,000-mark after more than one month.
Foreign Portfolio Investors infused Rs 362.79 crore last Friday, as per provisional data.