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.
Continued dollar buying by importers amid strong greenback overseas mainly weighed on the rupee.
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.
In the forward market, premia remained sluggish on persistent receiving by exporters.
The benchmark six-month premium payable in September declined to 221-223 paise from last weekend's close of 224.5-226.5 paise and forward contracts maturing in March 2016 also dipped to 443.5-445.5 paise from 457.5-459.5 paise.
The Reserve Bank of India fixed the reference rate for dollar at 62.3885 and for the euro at 66.1630.
The rupee reacted downwards against the pound sterling to 91.31 from 91.09 last Friday and fell back slightly against the Japanese yen to 51.79 per 100 yens from 51.76.
It, however, continued its upward march against the euro to 65.84 per euro 66.01 previously.