Earlier, the rupee opened higher at 64.13 against last closing level of 64.23 at the Interbank Foreign Exchange (Forex) market and firmed up further to 63.94 on persistent dollar selling before quoting at 63.98 at 1100 hours.
The rupee hovered in a range of 64.1750 and 63.94 during the late morning deals.
In the New York market, the dollar remained stuck in a range against most of its major rivals in early trade ahead of US jobs report later today, but sterling rallied to its highest in just over a week on expectations that British Prime Minister David Cameron's Conservatives will stay in office.