The flyover by Canberra by F-111 bombers was part of centenary celebrations for Australia's highest court. The display late on Saturday ended with the two jets lighting their afterburners in a fiery and noisy display.
Many residents mistook it for a new terrorist attack.
Jon Stanhope, chief minister of the Australian Capital Territory, said it had marred the centenary celebrations for the establishment of the High Court by needlessly causing "widespread fear and alarm".
"Given the proximity of the event to the anniversary of the Bali bombing, and generally heightened awareness of the risks of terrorism, the nature of the event was ill-considered and insensitive," he said.
"It was also badly planned and communicated, with very few people being aware in advance that a flyover was scheduled."
Stanhope said he would write to Attorney General Philip Ruddock and Defence Minister Robert Hill to complain.