Oil rose more than 1 percent on Monday after key OPEC producer Saudi Arabia pledged to cut exports in August to help reduce the global crude glut.
The local share price index futures rose 0.2 percent, or 13 points, to 5,638, a 50.1-point discount to the underlying S&P/ASX 200 index close.
The benchmark fell 0.6 percent to 5,688.1 on Monday.
New Zealand's benchmark S&P/NZX 50 index fell 0.08 percent in early trade.