The call follows the introduction of a bill to NSW Parliament's upper house by the Animal Justice Party that would ban mulesing by 2022.
Animal Justice Party MP Mark Pearson said moving away from mulesing made ethical and economic sense.
“The suffering we cause sheep in Australia, simply because we force them to exist in conditions intolerable to them, purely for human financial gain, is unconscionable,” he said.
AWU national secretary Daniel Walton said extensive consultation with shearers determined that banning mulesing would negatively affect the welfare of sheep.
“Shearers don't want to see animals suffer, and flystrike is capable of causing more suffering than just about anything else,” Mr Walton said.
“Mulesing is easily the most reliable and effective means of preventing flystrike.”
Mr Walton said alternatives like crutching, which involves frequent shearing, was unreliable.
“It also makes it difficult to enforce compliance in the instance of a regulatory regime, and therefore would compromise the health of sheep,” he said.
“However, there are legitimate concerns about the pain associated with the mulesing procedure and for that reason the union believes the most appropriate pathway forward should be to mandate anaesthesia procedures.”
Mr Walton said the majority of mulesed sheep were already receiving anaesthesia.
The AWU suggested a third-party body be established to work with government, industry and unions to develop a framework for delivering pain relief to sheep.