Western Australia's reputation as the world's deadliest place for shark attacks is hurting tourism and the federal government should consider lifting the ban on fishing of great whites, the state government says.

With the search called off on Sunday afternoon (WST) for the great white believed to have killed 24-year-old Perth man Ben Linden on Saturday, WA Fisheries Minister Norman Moore said he was "very distressed" by the death and the state's shark attack toll of five deaths in 10 months.

He issued orders on Saturday for staff from his department to kill any sharks measuring four to five metres in length - the estimated size of the shark that attacked Mr Linden - in the area of the latest attack.

Mr Linden had been surfing near Wedge Island, 160km north of Perth, earlier that morning.

"Five fatalities in Western Australia (in 10 months) is unprecedented and cause for great alarm," Mr Moore told reporters.

"It won't be helping our tourism industry and those people who want to come here to enjoy an ocean experience will be turned away because of this situation."

Fisheries officials called off the hunt on Sunday afternoon because they had not seen any large sharks in the area, but Mr Moore said he would lift a protection order on great whites if the federal government did the same.

He said he would lobby Canberra to allow commercial and recreational fishing of the species, saying there was anecdotal evidence great white numbers had recovered significantly since they were first protected in Australia in the 1990s.

However, he would not be sanctioning state shark hunts or culls.

Shark nets were not the answer, either, as they killed whales and other marine life.

Mr Moore said the community was "divided" over reducing great white shark numbers and that more research was needed to plot their migration and feeding habits.

Swimmers and surfers could reduce the risk of attack by not entering the water at dawn, dusk or on overcast days, the fisheries minister said.

"Regrettably, people are being taken by sharks in numbers which we have never seen before," he said.

"We need to try to work out to the best of our capacity what is causing this to happen.

"I'm totally perplexed."

Although the hunt for the shark was called off, local police and volunteers are expected to continue to comb beaches for the young man's remains, which have yet to be recovered, while beaches in the immediate area will remain closed for at least two days.

Mr Linden was surfing with a mate on Saturday about 100m from shore, 4km south of Wedge Island, when he was attacked by what was described as a "massive" white pointer at about 9am (WST), becoming the fifth shark fatality in WA's southwest in just 10 months.

Surfers in the area said they had noticed a large shark in the vicinity in the previous four days and had nicknamed it "Brutus" because of its large size.

Following the most recent death of 33-year-old diver Peter Kurmann near Bunbury on March 31, Fisheries senior shark research scientist Rory McAuley described WA's southwest coast as the deadliest place in the world for shark attacks.

Mr Moore said people should report shark sightings and, if the fish was a danger to humans, he would order its destruction.

Tributes continued to flow in for Mr Linden on Sunday, after his long-term girlfriend Alana Noakes reported his death on his Facebook page.

Cabinet-maker Mr Linden was also a singer and bassist in Perth band Fools Rush In, which featured on radio triple J's national unearthed segment.

AAP