Australia averages fewer than two fatal shark attacks a year nationwide.
The state government has promised to hunt the killer and is considering more aircraft surveillance off west coast beaches as whales migrating in larger numbers attract more sharks.
The first sign that the 32-year-old American man, whose name and hometown have not been released, was in trouble as he dived alone was when a stream of bubbles erupted on the ocean surface beside his 25-foot (8-meter) dive boat, police said.
His two horrified companions on the boat saw his lifeless body surface and a 10-foot (3-meter) great white swim away, Western Australia Police Sgt. Gerry Cassidy said.
The shark struck 500 yards (meters) north of the picturesque tourist haven of Rottnest Island, which is 11 miles (18 kilometers) west of a popular Perth city beach where a 64-year-old Australian swimmer is believed to have been taken by a great white on Oct. 10.
Authorities cannot say whether the American was killed by the same shark that is believed to have taken Bryn Martin as he made his regular morning swim from Perth's Cottesloe Beach toward a buoy about 380 yards (350 meters) offshore.
But an analysis of Martin's torn swimming trunks recovered from the seabed near the buoy pointed to a great white shark being the culprit. No other trace of Martin has been found.
"It's a cloudy old day today which is the same as we had the other day with Cottesloe, and they're the conditions that sharks love," Cassidy said.
The American had a work visa and had been living in a Perth beachside suburb north of Cottesloe for several months.
The tragedies follow the death on Sept. 4 of 21-year-old bodyboarder Kyle Burden, whose legs were bitten off 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.
Perth, the capital of Western Australia state and one of Australia's largest cities, is renowned for its white sand beaches, but the best surfing locations are further south in the wine region of Margaret River.
While great whites trail the migration of whales between Antarctic and northwest Australian waters, the west coast has not been widely regarded as a shark danger zone for humans.
Premier Colin Barnett, the leader of the state government, took charge of the official response on Saturday, telling reporters that the shark will be hunted and killed if possible.
He said fisheries officers will spread bait in the area of the attack to try to catch the shark.
While great whites are protected under Australian law, Barnett said his government would consider increasing the numbers of other sharks that commercial fishermen can catch, following reports that shark numbers have increased.
He said his government was also looking at increasing aerial shark patrols over popular beaches.
"I think all West Australians need to take special care in going to the beach and swimming, particularly if they go diving," he said.
Barnett said he did not expect the fatalities would damage the state's tourism reputation or diminish people's enjoyment of the beaches.
Barbara Weuringer, a University of Western Australia marine zoologist and shark researcher, urged against a shark hunt, saying there was no way of telling which shark was the killer without killing it and opening its stomach.
"It sounds a little bit like taking revenge and we're talking about an endangered species," Weuringer said Sunday.
She said the increase in shark attacks could reflect the human population increase in the southwest. A more productive response would be to bring forward shark spotting flights from their November start date.
But a southwest coast-based diving tourism operator has called on the state government to kill sharks that pose a threat to humans.
"We suggest the Department of Fisheries treat sightings of great whites close to shore or aggressively approaching boats in inshore waters as an opportunity to dispatch that individual shark and prevent the risk of future attack," Rockingham Wild Encounters director Terry Howson told Perth's Sunday Times newspaper.
Great whites can grow to more than 20 feet long (6 meters) and 5,000 pounds (2,300 kilos). They are protected in Australia, a primary location for the species.
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