Currency traders said weakness in the dollar against major world currencies overseas supported the rupee.
A higher opening in the domestic equity market gave the uptrend some momentum, they added.
Yesterday, the rupee had declined by 11 paise to close at 64.02 against the US dollar amid renewed global tensions in the wake of North Korea firing a missile that passed over Japan.
Meanwhile, the benchmark BSE Sensex rebounded by 193.39 points, or 0.61 per cent, to 31,581.78 in early session today.