The Western Australian Government has given the go-ahead for any great white sharks to be killed if they pose a threat to human life.

It is believed a three-metre great white was responsible for the fatal attack on 32-year-old American George Thomas Wainwright on Saturday at Rottnest Island.

Fisheries officers spent the day on Sunday trying to catch the shark, but have so far failed in their attempt.

A three-metre shark was spotted at the popular Thompsons Bay on Sunday and Rottnest beaches remain closed.

"Whether it's the one that was involved ... with the fatal attack we're unsure at this time," said Police Media's Jill Willoughby, adding that fisheries officers were heading to the area.

Fisheries Minister Norman Moore says although great whites are an endangered species, with three fatalities in less than two months, the government has to act.

"It will remain the case in the future that in the event that a great white is a threat to human life and I'm advised of it, then I will give authority to the fisheries department to seek to catch that shark and to destroy it," he said.

Mr Wainwright was diving about 500 metres off shore at Little Armstrong Bay when his body surfaced with horrific injuries.

Friends of Mr Wainwright said the shark had nudged their vessel shortly after he was killed.

Mr Wainwright was a US citizen from Texas, but had been working in Australia for six months and living in North Beach.

His immediate family in America have been told of his death.

It is the third suspected fatal shark attack in the state's waters in less than two months.

Earlier, Premier Colin Barnett said his government would consider shark culls in the future following the latest shark attack.

He described the American's death as "tragic" and ordered that the shark responsible to be caught and killed.

But he said the Government will be cautious when considering shark culls.

"We'll certainly look at that as a government, but I don't think we [should] rush into that. We'll look at the situation very carefully," he said.