State and territory governments are considering clamping down on gun licences and banning non-citizens from owning firearms in response to the Bondi Beach massacre, the nation's worst mass shooting in nearly 30 years.
Executive Council of Australian Jewry boss Daniel Aghion said political leaders shouldn't forget the cultural changes needed to tackle hatred against Jews.
"You're talking about the difference between motive and act," he told AAP.
"The gun facilitates the act, but it does not give the motive for the attack.
"The motive here is the hatred of Jews. That's the open wound that this country needs to deal with."
Former prime minister John Howard, who overhauled Australia's gun laws after the 1996 Port Arthur massacre, said he would support sensible tightening of his landmark reforms.
But he also warned Anthony Albanese not to use firearms reform as a "diversion" from tackling anti-Semitism.
Mr Albanese said his government was doing what it could to fight hatred against Jews, but anti-Semitism had been around for a long time.
Opposition Leader Sussan Ley accused the government of not doing enough on the issue.
"We can't afford to have an approach by the government that treats anti-Semitism as a problem to be managed, not an evil to be eradicated," she told ABC News.
Ms Ley has set up an internal task force to develop policies on counter terrorism, deradicalisation and anti-Semitism.
The group of shadow ministers will meet with the government's special envoy to combat anti-Semitism Jillian Segal on Wednesday, and plan to also sit down with other Jewish leaders.
Two Liberal backbenchers told AAP they had not been told about the task force before details of the policy were disseminated to media.
Because one of the Bondi shooters was born overseas, conservatives in the party are using the massacre to push for a reinvigorated debate over migration.
Ms Ley had planned to announce the core principles of her immigration policy before Christmas, but those plans had been put "on ice" because of the attack, a senior Liberal source said.
Ms Segal handed her report on anti-Semitism to the government in July, but many of its recommendations are still unaddressed.
She said she was preparing a new policy document following the Bondi attacks.
"I hope that they will follow that and will deal with some of these difficult questions as to where you draw the line," Ms Segal told Sky News.
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