Moore, who has called on the federal Government to review the great white's protected status, said shark nets were not the answer becausethey killed whales and other marine life.
And while he wants the ban on commercial and recreational fishing of great whites to be lifted, he ruled out state-sanctioned shark hunts or culls.
The ban was imposed in the mid-1990s amid concern about the dwindling population. Moore said anecdotal evidence now suggested that it had recovered significantly.
Tony Burke, the federal Environment Minister, said he would consider any proposal by the WA Government. But Nic Dunlop, a spokesman for the Conservation Council of WA, said it was "biologically impossible" for shark numbers to have increased substantially in 15 years.
Five fatal shark attacks took place in WA waters between November 2000 and August 2010, compared with the five since last September. Moore said more research was needed to plot the great whites' migration and feeding habits.
Holmes told the Australian that the attack on Linden was like a Jaws movie. When the shark tried to knock him off his jet-ski, he said, "it was like it was protecting its food".
Although the hunt for the shark was called off on Sunday afternoon, beaches in the area remained closed yesterday. Five shark warning signs have been stolen since the attack.
Prime Minister Julia Gillard said she understood the WA Government's push to protect beachgoers from sharks.
A Department of Fisheries spokesman said if another big great white was seen, action could be taken because there were exemptions to its protection in circumstances of immediate danger to humans.
- additional reporting AAP