Federal Environment Minister Tony Burke has the left the way open to removing white pointer sharks from the protected species list, backing efforts to find out whether the animal's stocks are increasing.
A day after WA Fisheries Minister Norman Moore said he would write to the Commonwealth asking if great white sharks should still be protected, Mr Burke said he agreed their numbers needed to be better understood.
"There is a view among some that shark numbers have increased and I know both governments will work together to get as clear a picture as possible about whether the great white shark population is recovering," Mr Burke said.
But in a sign of the challenge facing authorities, the head of WA's Fisheries Department said it was "extremely" difficult to estimate the population of great whites because they were so mobile.
Stuart Smith said it was possible to reasonably gauge the number of white pointers around Australia at any one time, but this figure was liable to change because the predators travelled between continents.
"Any number you come up with is probably only valid for that moment because they migrate so much," he said.
"So getting a handle on how many are here as opposed to South Africa, or how many are on the east coast versus New Zealand, is almost impossible."
There was also a mixed response to whether lifting the ban on killing great whites would be effective in reducing their numbers amid universal agreement they held almost no commercial value.
Augusta shark fisherman Jeff Cooke said great whites invariably had unacceptably high mercury levels in their bodies because of their size and could therefore not be sold for eating.
Former professional angler Peter Glass, who operated out of Geraldton, said lifting the ban on killing great whites would only encourage "weekend heroes" who wanted to be "on the front of the paper".