He is not labelling it a shark cull, but Western Australian Premier Colin Barnett says the state government may change laws so sharks lingering near the southwest coast can be killed.
Some surfers have demanded a shark cull after another fatal attack at the weekend and Mr Barnett says options are being considered.
"I don't know if it's a cull as such - and maybe that means different things to different people - but I certainly acknowledge that the public is demanding that sharks, where they stay around popular swimming or surfing areas, should be destroyed. I'm in that camp," he said.
However, such a measure was not necessarily going to be implemented, Mr Barnett said.
"I want to reassure people that the shark patrols using helicopters have been effective in spotting sharks and if you swim at beaches that are patrolled and stay within those areas, you are safe."
"The risk is for people going out and surfing ... or going and diving on reefs off the coast. That is where the real danger is."
Mr Barnett said the state government would need to seek federal government approval to kill great white sharks because they were a protected species.
"Where it's deemed to be an imminent danger, we can proceed if it's a matter of destroying the shark," he said.
"It may be that we will widen the definition of imminent danger."
But Fisheries Shark Response Unit spokesman Tony Cappelluti said culling had not been researched.
Mr Cappelluti said the department had tagged 338 sharks - 140 of which were great whites.
He said the department would also keep a closer eye on beaches in the southwest while school leavers were there this week.
Chris Boyd, 35, was surfing at popular surf break Umbies off Gracetown when a suspected great white shark bounced off another surfer's board and attacked him on Saturday morning.
Anaesthetist Dennis Millard, who was surfing near Mr Boyd, said it was all over very fast and there was not much he could do to help the 35-year-old father of two.
"I think it would have been very painless and quick," he told reporters.
The doctor has since bonded with the Boyd family.
"He was an absolute water man, who was a warrior of the ocean."
An imminent threat order issued after the shark attack was rescinded on Monday night after the department failed to catch a shark potentially responsible for the attack.
Mr Boyd's death is WA's first fatal shark attack this year.
It comes weeks after abalone diver Greg Pickering was bitten by a five-metre great white while diving off the coast of Esperance.
There have been three fatal shark attacks in Gracetown in the past 10 years.
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