But a southwest coast-based diving tourism operator called on the state government to kill sharks that pose a threat to humans.
"The nuisance sharks — the problem sharks that move into an area and are aggressive — should be dispatched to remove the risk of future attack," Rockingham Wild Encounters director Terry Howson told the AP.
Howson has been campaigning for government action on sharks since one of his tour guides, Elyse Frankcom, was injured in a shark attack last year.
"It's absolutely hurting the tourist trade," he said. "Australia is getting a name for itself as being full of dangerous animals."
Wainwright's two companions said the diver was already dead when his body surfaced beside their boat moments after a flurry of bubbles had erupted on the gray ocean surface.
The shark, a 10-foot (3-meter) great white, surfaced and even nudged the dive boat as Wainwright's friends hauled in his remains and powered for shore, officials said.
A great white of the same size is believed to have taken a 64-year-old Australian swimmer off Perth city's premier Cottesloe Beach on Oct. 10. The beach is 11 miles (18 kilometers) east of Rottnest Island.
The man's remains were not found, but his shredded swimming trunks suggested the size and type of shark that took him.
Both attacks followed the Sept. 4 death of a bodyboarder attacked by a shark described as 15 feet (4.5 meters) long at a beach south of Perth. Witnesses were unsure of the type of shark.
The continent averages little more than one fatal attack a year along an expansive 22,000-mile (35,000 kilometer) coast. But it is a primary home of the fearsome great whites, a large species in which some animals can grow to 20 feet (6 meters) in length.
The film classic "Jaws" famously used a mechanical shark for close-up action, but live shark footage was filmed in Australia. One is a scene in which Richard Dreyfuss is in an underwater shark cage, and live sharks doubled for the movie killer in long-range shots as well.
Associated Press writer Kelli Kennedy in Miami contributed to this report.