Earlier, the domestic unit opened higher at 64.77 per dollar as against last Friday's closing level of 64.81 at the Interbank Foreign Exchange (Forex) market.
Later, it fell on fresh dollar demand by importers to Rs 64.85 before quoting at 64.79 at 1030 hours.
The domestic unit is hovering in a range of 64.85 to 64.73 during the morning deals.
"The rupee is expected in a range 64.65-64.95 per dollar for the day. Upticks will attract selling interest from exporters as they hedge their future receivables," a forex dealer said.
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The dollar index is currently trading down by 0.02 per cent at 94.66 as against a basket of six currencies.
Overseas, the dollar gained as traders reckoned that the US Fed might raise interest rates later this year and the European Central Bank may provide more stimulus to help the euro zone economy.
Oil prices slipped in early Asian trade, wiping out some of the previous session's gains, as investors digested the Chinese GDP data for the third quarter.