A search continues for the 63-year-old man who police confirmed died in the attack off Perth's Sorrento Beach about 10.30am on Friday.
Police confirmed he had not been found in an air and sea search on Friday or in a shoreline search on Saturday morning.
It is the second shark attack off WA's coast in five days.
WA Primary Industries Minister Jackie Jarvis told reporters on Saturday the government extended its condolences to the man's family.
"This is an incredibly sad and distressing incident and my thoughts are with everyone who knew and loved him," she said.
WA Police had requested the shark be captured and killed to assist with the recovery of coronial evidence, Ms Jarvis said.
"Given that the shark had been positively identified, remained in the vicinity following a fatal attack and was considered to pose an ongoing threat, I authorised fisheries officers to destroy the shark if it could be captured," she said.
Drumline capture gear would be deployed, Ms Jarvis said, noting it would be difficult to catch a white shark more than three metres long.
She said the government had a comprehensive shark mitigation program that was constantly reviewed but could never eliminate all risks for water users.
"We will see what more we can do," she said.
"I cannot remove the risk of all apex predators in the ocean."
A witness told ABC News on Friday she was alerted to the attack when she was walking along the beach and saw a pool of blood in the water.
The City of Joondalup closed all beaches in the area, from Burns Beach in the north to Marmion in the south, until midday on Saturday as a precaution.
The fatality follows a shark attack on a surfer at a remote WA beach on Monday.
The man was seriously injured at Glenfield Beach, north of Geraldton in the state's Mid West
He was taken to the nearby Geraldton Health Campus and is in stable condition.
Surf Lifesaving WA's helicopter shark patrols began for summer last week.
They will initially operate on weekends before becoming daily between Mandurah and Yanchep, and Rottnest Island to the west, from September 26 until the end of April.
Patrol flights in WA's southwest between Bunbury and Hamelin Bay will run daily during school holidays and peak summer periods, and on weekends and public holidays at other times.
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