Dealers said the strength in the rupee was also supported by increased selling of dollars by exporters and the American currency's weakness against some currencies overseas.
A higher opening of the domestic equity market too influenced the rupee, they said.
The benchmark BSE Sensex was up 67.09 points, or 0.19 per cent, to quote at 35,209.08 in early trade.
The rupee had gained 36 paise to end at 72.31 against the US dollar Wednesday as global crude oil prices hovered near one-year lows, easing concerns over expanding current account deficit and inflation.
Brent crude, the international benchmark, fell eased by 0.47 per cent to $65.81 a barrel.