According to forex dealers, fresh selling of the American currency by exporters and banks caused by its weakness overseas gave the rupee strength.
A higher opening in the domestic equity market only fuelled the uptrend.
Yesterday, the rupee had shed 2 paise to close at 64.55 against the greenback in limited trade on the back of stray dollar demand from importers.
In early trade today, the benchmark Sensex rose 159.85 points, or 0.51 per cent, to 30,994.17.