Australia's parliament has voted for sweeping gun law reforms and a crackdown on hate speech, a month after two attackers shot 15 people dead at a Jewish festival at Bondi Beach.

Both bills passed the House of Representatives and Senate at a special sitting late on Tuesday. The gun reform measures include a national gun buyback scheme and new checks on firearm licence applications.

Home Affairs Minister Tony Burke said the Bondi gunmen would not legally have had access to firearms if such a law had been in place prior to the attack, the country's worst mass shooting in decades.

Governing Labor senators were backed on the anti-hate bill by Liberal lawmakers, whose coalition partners abstained.

After last month's mass shooting, Prime Minister Anthony Albanese came under huge pressure for not having done enough to prevent the attack in the first place, amid growing fears of antisemitism in the Jewish community.

Politicians were recalled two weeks early to debate the legislation. Introducing the reforms, Burke said individuals with hate in their hearts and guns in their hands had carried out the 14 December attack.

The father in the father-son duo allegedly behind the attack legally owned six firearms, while his son had been on the radar of intelligence agencies.

The gun reform bill, which cleared the House of Representatives by 96 votes to 45, includes stricter firearm import controls and provisions to improve information sharing between intelligence agencies on people trying to obtain gun licences.

The buyback scheme will target surplus and newly restricted firearms, Burke said, reducing the country's four million registered guns.

Burke added that it comes as a shock to most Australians to know that the country has more firearms than it did before the 1996 Port Arthur attack, which resulted in 35 deaths. This new law will bring significant changes to Australia’s gun laws since then.

The hate speech reforms had initially been part of a larger bill with the gun reforms but were split after opposition from some parties. Despite uncertainties, a revised version garnered support and was passed with provisions targeting hate groups and advocating violence.

The bill ensures regular reviews and consultations regarding extremist organization listings with the opposition involved.