Banks and exporters preferred to reduce their dollar position in view of lower greenback demand in overseas market.
The unit continued to weaken in the global market, sending a benchmark dollar index to the lowest level since late January as recent sluggish US data prompt investors to rethink the timing of the first Federal Reserve rate hike.
The dollar index was trading down 0.38 per cent against its major global rivals.
In New York market, the US dollar weakened against most of its major rivals yesterday after a slate of disappointing economic data.
The rupee opened higher at 63.97 per dollar against the last closing level of 64.00 at the Interbank Foreign Exchange Market and hovered in a range of 63.61 and 64.04 before concluding the day at 63.65, showing a gain of 35 paise or 0.55 per cent.
The rupee has increased by 52 paise or 0.81 per cent in the last two sessions.
In an irregular trade, the Indian benchmark Sensex on Thursday trimmed major part of its early losses on hopes of rates cut by the central bank following fall in inflation data.