The rupee was trading at 58.87/88 per dollar by 0615 GMT, off its session high of 58.62, its highest since June 19. The currency closed at 59.29/30 on Thursday.
The rupee gained after early counting showed Narendra Modi's Bharatiya Janata Party and its allies leading in 335 seats, way above the 272 seats required to win a majority in the lower house.
Traders however said dollar buying was sporadic and not as aggressive as in recent sessions.
The main share index was trading up 3.7 percent, after earlier rising as high as 6.15 percent.