Forex dealers said weakness in the greenback against other currencies overseas gave the rupee some relief.
Further, a higher opening in the domestic equity market gave the uptrend some momentum, they added.
On Wednesday, the domestic unit ended higher by 28 paise at 68.05 following a fresh bout of dollar selling.
Meanwhile, the benchmark BSE Sensex rose 171.39 points, or 0.64 per cent, to 26,804.52, in early session today.