At the Interbank Foreign Exchange (Forex) market, the domestic unit commenced better at 60.10 a dollar from previous close of 60.18.
It was trapped in a narrow range of 60.05 and 60.27 before settling at 60.20, a fall of a mere two paise or 0.03 per cent. On Friday, it fell by 10 paise.
Sustained dollar demand from importers, mainly oil refiners, weighed on the rupee, a forex dealer said.
The benchmark S&P BSE Sensex today moved down further by 74.19 points, or 0.30 per cent. FIIs had pulled out Rs 220.65 crore last Friday, as per provisional data with exchanges.
The dollar index was marginally down against its major global rivals.
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