They rejected a bid from conservation groups to have the programme suspended.
Over 100 sharks larger than 3 metres have been caught and killed since a cull was announced in January in the wake of seven fatal attacks in three years.
The Environmental Protection Authority (EPA) in West Australia received 23,000 submissions, most demanding the cull be stopped, when it asked for community views during February but has declined calls to intervene.
"This isn't an opinion poll," authority chief Paul Vogel told national broadcaster ABC. "The risk assessment we got said there was a negligible risk to target and non-target species of sharks."
The state government received a waiver from federal environmental legislation to run the cull until April 30.
There have been protests all round Australia over the killing of sharks using baited hooks tethered off popular beaches.
Last week environmental group Sea Shepherd Australia lost a legal challenge to the programme.
The Conservation Council of Western Australia, which has received over 6,000 signatures to its petition to stop the cull, urged the EPA to reconsider its decision.