Forex dealers said apart from fresh inflows from foreign funds, dollar's weakness against some other currencies overseas provided added momentum to the rupee.
The domestic unit ended steady at 67.95 a dollar on Tuesday following fag-end dollar demand from banks and importers in view of uncertainty in the currency market.
It finally settled at 67.68 per dollar, showing a gain of 27 paise or 0.40 per cent.
The Indian rupee strengthened on Wednesday by 26 paise to 67.68-69 against a U.S. dollar from its previous close of 67.95 in line with a weakness in the greenback against a host of Asian currencies.
The dollar index was trading down 0.25 per cent against a basket of six currencies in the late afternoon trade.
The RBI fixed the reference rate for the dollar at 67.6166 and euro at 75.0071.
At overseas, the British pound traded higher for a third session today as fading fears over Brexit heightened investors' appetite for what are typically riskier assets. The benchmark six-month premium for November fell to to 174-176 paise from the last weekend's level of 178-180 paise and far forward May 2017 contract also eased to 367-369 paise from 371-373.