The Australian share market has bounced back from its sharp morning losses as it become apparent that an Iranian missile attack on US forces in Iraq had not caused casualties.

After being down as much as 76 points shortly before noon on Wednesday, the benchmark S&P/ASX200 index mostly recovered to finish down just 8.8 points, or 0.13 per cent, to 6,817.6 points.

The broader All Ordinaries closed down 13.5 points, or 0.19 per cent, to 6,930.1 points.

Meanwhile, the Australian dollar was buying 68.72 US cents, down from 69.17 US cents when the ASX closed on Tuesday.