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.
"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.
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"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.
FIIs had picked up shares worth Rs 943.19 crore last Friday, as per provisional data.