Besides, robust capital inflows and rallying local equity markets supported the trading sentiment, forex dealers said.
Overall sentiment was largely optimistic following upbeat comments from Reserve Bank Governor Raghuram Rajan that the economy is picking up and the country can withstand any crisis emerging from the Greek fallout.
Extending its strong upmove, the rupee resumed firmly higher at 63.43 against Thursday's close of 63.51 at the Interbank Foreign Exchange market and strengthened further to hit fresh intra-day high of 63.35 before finishing at 63.44.
It registered a gain of 7 paise, or 0.11 per cent, a level not seen since May 5 this year.
The US dollar index was down by 0.10 per cent at 96.19.
Crude prices eased after a brief overnight spike amid a glut of over-supply in global markets as well as lacklustre US macro data.
Meanwhile, foreign investors bought shares worth Rs 575.3 crore yesterday, according to provisional data.