The currency was underpinned by foreign inflows into equity markets for a third straight session. Overseas investors bought shares worth $32.35 million on Wednesday, provisional data from the exchange showed.
Broader gains were capped as the market focuses on the government's policies which will be unveiled in the Budget, likely in early or mid-July.
Alongside, the RBIs frequent interventions in the forex market to stem sharper gains in the rupee, weighed on sentiment.
The RBI's dollar purchases in the spot market and the corresponding paying in the forwards to mitigate the impact on liquidity have been pushing up the forward premiums.
"The inflows will continue in the near term and may get better direction after the Budget. RBI doesn't seem to allow sharp appreciation of the rupee through intervening," said Paresh Nayar, head of fixed income and foreign exchange trading at First Rand Bank, adding he expects the pair in a range of 58.50/60.00 in the coming weeks.
The partially convertible rupee closed steady at 59.33/34 per dollar.