Earlier, the rupee had opened weak at 64.09 on sustained dollar demand against the overnight closing of 64.04 at the Interbank Foreign Exchange (Forex) market.
It moved in a range of 64.09 and 63.97 per dollar during the morning deals before quoting at 63.97 at 1025 hours.
The dollar index was up 0.13 per cent at 97.58 against a basket of six currencies in the early trade.
Oil prices edged up in early Asian trade following a 5 per cent fall in the previous session as high global production and a weakening economic outlook, especially in Asia, prompted analysts to caution further falls.
Meanwhile, the benchmark 30-share index was trading down 145 points, or 0.51 per cent, to 28,041.97 at 1030hrs.