Forex dealers said weakness in the dollar against other currencies overseas supported the rupee.
Further, a higher opening in the domestic equity market gave the uptrend some momentum, they added.
On Thursday, the domestic unit ended higher by 6 paise at 67.05 against the greenback on bouts of dollar selling by banks and exporters.
Meanwhile, the benchmark BSE Sensex rose 84.81 points, or 0.30 per cent, to 27,920.72, in early session on Friday.
PTI