By Dominic Giannini and Andrew Brown in Canberra

Hate preachers and those celebrating violence have been warned they will be targets as Labor pledges to push laws to their constitutional limit to crack down on anti-Semitism.

Prime Minister Anthony Albanese’s policy suite to tackle anti-Semitism in the wake of Bondi’s massacre includes tightening hate speech laws, implementing stronger firearm restrictions and introducing a gun buyback scheme.

Home Affairs Minister Tony Burke vowed to lower the threshold of hate speech laws “to the extent that constitutionally we are able to”.

Australian Federal Police Commissioner Krissy Barrett said the move, in conjunction with extra resources, would make it easier to take action more quickly.

“This is all about stopping hate and division earlier, and well before it leads to violence,” she told reporters on Friday while standing alongside the prime minister.

“History has taught us and recent events have reinforced that hatred creates a permissive environment that can lead to violent extremism and terrorism.”

Four people had been charged with anti-Semitism-related offences by a national investigation team set up to address politically motivated violence and hate speech that didn’t meet the threshold for terrorism investigations, Ms Barrett revealed.

The prime minister visited the Canberra headquarters of the federal police and ASIO on Friday for updates on the Bondi shooting investigation, while the national security committee has met six times in the wake of Sunday’s attack.

Two Islamic State-inspired gunmen killed 15 people and injured dozens more when they targeted Hanukkah revellers in the massacre.

The prime minister stood firm against opposition calls to recall parliament before Christmas to pass the suite of legislation, saying it was important to ensure the laws could stand up to a potential High Court challenge.

“There are constitutional issues, there are issues of free speech involved in this as well,” he said.

“We’re going to make sure that these laws don’t get passed and then get knocked over.”

Parliament is scheduled to resume in early February.

Opposition Leader Sussan Ley branded Labor’s anti-Semitism response “too little, too late”.

She unveiled her own policy response, which includes expanding offences for which dual nationals could have their citizenship stripped and strengthening powers to deny and cancel visas for those who preach or engage in anti-Semitism.

“Enough has not been done to silence hate preachers and tackle radical Islam,” she told reporters at Bondi.

Mr Albanese was quick to point out the coalition pushed to weaken anti-discrimination laws due to free speech concerns when questioned about why he didn’t strengthen anti-hate laws earlier.

He said bipartisanship was needed following the act of terror in Bondi, the deadliest attack in Australia since Port Arthur in 1996.

The opposition hasn’t committed to supporting tighter gun restrictions, with junior coalition partner the Nationals opposed to some measures like stringent ownership caps.

The government has announced a $42.6 million package for extra mental health support for those traumatised by the attack.