The rupee resumed lower at 60.12 per dollar at the Interbank Foreign Exchange (Forex) from its last Friday's closing level of Rs 60.10 per dollar.
It gained later and was quoting at 60.08 per dollar at 1020 hours.
The domestic unit moved in a range of 60.08 and 60.13 per dollar during the morning trade.
In New York, the dollar was up last Friday against its major rivals following weak German economic data.