The rupee fell despite the stock benchmark Sensex ending above the 26,000-level for the first time in its history ahead of the Union Budget.
At the Interbank Foreign Exchange (Forex) market, the domestic unit commenced lower at 59.80, which was also its day's high, from last Friday's close of 59.72. It declined further to a low of 60.04, before concluding at 60.01 a fall of 29 paise or 0.49 per cent.
Previously, it had tumbled by 36 paise or 0.60 per cent on June 18, 2014.
"Due to a firm US Dollar in the global market and demand for the Greenback in the domestic market from the custodian banks, the rupee fell... It did not draw cues from the upswing in the domestic equity markets," said Anindya Banerjee, currency analyst, Kotak Securities.
The dollar index, however, was trading down by 0.03 per cent against its major global rivals.
"It was a weak session for the rupee. It started the day on a slightly weaker note with dollar index trading above its one week high and euro trading near its two week low. Now the markets will be waiting for the budget to be presented on 10th July by the new government to get further cues," said Abhishek Goenka, Founder & CEO, India Forex Advisors.
The benchmark S&P BSE Sensex today rose by 138.02 points or 0.53 per cent to settle at new peak of 26,100.08.
FIIs had picked up shares worth Rs 943.19 crore last Friday, as per provisional data.
"Mismatch in demand and supply of dollar on account of US markets holiday may be the reason for this sharp depreciation. Most of the Asian currencies are weaker against dollar," said Kiran Kumar Kavikondala, Director & CEO, WealthRays Securities.
Meanwhile, the premium for forward dollar remained weak on continued receipts by exporters.
The benchmark six-month premium payable in December eased to 248-250 paise from previous close of 251.5-253.5 paise.
Far-forward contracts maturing in June, 2015 also dropped to 495-497 paise from 498.5-501.5 paise.
The Reserve Bank of India fixed the reference rate for dollar at 59.9455 and for the euro at 81.3923.
The rupee dipped further against the pound to 102.79 from 102.35 previously while fell back to 81.60 per euro from 81.18. It also declined to 58.87 per 100 Japanese yen from 58.52.