The rupee pared its early gains, but was still trading up by 2 paise at 64.79 against the US currency in late-morning deals on bouts of dollar selling by banks and exporters.
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.
"On the lower side, it is most likely that we see dollar buying interest come in from local government banks on account of their regular demand."
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.
Meanwhile, the benchmark BSE Sensex was trading higher by 70.38 points, or 0.26 per cent, at 27,284.98 at 1035 hours.
