The rupee resumed lower at 63.65 as against yesterday's level of 63.59 at the Interbank Foreign Exchange (Forex) market.
It hovered in a range of 63.57 and 63.70 during the day before closing the day at 63.60.
The dollar index was trading lower by 0.20 per cent against its major global rivals today.
In the New York market, the dollar rose against the euro yesterday, after a strong new-home sales report and hawkish comments from US Federal Reserve governor Jerome Powell shifted investors' rate-hike expectations towards the central bank's September meeting.
Meanwhile, the benchmark BSE Sensex snapped its 8-day winning spree, ending lower by 74.70 points, or 0.27 per cent, to settle at 27,729.67.