At noon AEDT on Tuesday, the benchmark S&P/ASX200 index was up two points, or 0.02 per cent, to 8,207.4, while the broader All Ordinaries was down 1.3 points, or 0.02 per cent, to 8,477.7.
Brent crude rose to a six-week high of $US81 a barrel overnight, up from around $US75 last week, as Hezbollah fired more rockets at Israel, which seemed prepared to launch major new offensives in both northern Gaza and Lebanon.
Storm clouds and a recipe of caution and potential pullbacks were hanging over markets, Moomoo market strategist Jessica Amir said.
In addition, a strong monthly US jobs report showed the Federal Reserve may not need to go full throttle in cutting interest rates, she added.
At midday five of the ASX's 11 sectors were higher and four were lower, with industrials and health care basically flat.
Tech was the biggest mover, dropping 1.5 per cent. Technology One was down 2.6 per cent and Xero had fallen 2.3 per cent.
In the heavyweight mining sector, Rio Tinto had gained 1.2 per cent, BHP had dipped 0.1 per cent and Northern Star had fallen 1.6 per cent.
West African Resources had made up some of Monday's plunge, rebounding 10.3 per cent, after the goldminer said authorities in Burkina Faso had assured it that its mining permits there were in good standing.
The nation also explained that junta leader Ibrahim Traoré's comments about revoking permits only applied to companies violating the law, the goldminer said.
In the energy sector, Woodside was up 0.6 per cent and Santos had gained 0.9 per cent amid the jump in oil prices.
The big four banks were mostly lower, with CBA down 0.4 per cent, Westpac dipping 0.3 per cent and NAB edging 0.1 per cent lower. ANZ was the exception, up 0.1 per cent.
The Australian dollar had dropped to a fresh three-week low against its US counterpart, buying 67.60 US cents, from 68.04 US cents at Monday's ASX close.