Sajid Akram and his son Naveed opened fire on Jewish crowds thronging the famous beach for Hanukkah on Sunday evening, killing 15 people and wounding dozens more.

Authorities said the attack was designed to sow panic among the nation's Jews, but have so far given little detail about the gunmen's deeper motivations.

Albanese gave one of the first hints that the pair had been radicalized by an "ideology of hate".

"It would appear that this was motivated by Islamic State ideology," Albanese told national broadcaster ABC.

"With the rise of ISIS more than a decade ago now, the world has been grappling with extremism and this hateful ideology," he said in a separate interview.

Police found a car registered to Naveed Akram parked near the beach in the aftermath of the shooting.

They found improvised bombs and "two homemade ISIS flags", New South Wales Police Commissioner Mal Lanyon said on Tuesday, using another name for the Islamic State group. 

Authorities are facing mounting questions over whether they could have acted earlier to foil the attack.

Albanese said Naveed Akram, reportedly an unemployed bricklayer, had come to the attention of Australia's intelligence agency in 2019 but was not considered an imminent threat at the time.

"They interviewed him, they interviewed his family members, they interviewed people around him," Albanese said.

"He was not seen at that time to be a person of interest."

Police are still piecing together the duo's movements before the shooting.

A key question is whether they met with Islamist extremists on a trip to the Philippines last month, Australian media reported.

"The reasons why they went to the Philippines, and the purpose of that, and where they went, is under investigation at the moment," Lanyon told reporters on Tuesday.

Naveed reportedly told his mother on the day of the attack that he was heading out of the city on a fishing trip. 

Instead, authorities believe that he was holed up in a rental apartment with his father plotting the assault.

Carrying long-barreled guns, they peppered the beach and a nearby park with bullets for 10 minutes before police shot and killed 50-year-old Sajid.

Naveed, 24, remains in a coma in hospital under police guard.

A 10-year-old girl, a Holocaust survivor and a local rabbi were among those killed, while 42 others were rushed to hospital with gunshot wounds and other injuries.

Australia's leaders agreed on Monday to toughen laws that allowed father Sajid to own six guns.

Mass shootings have been rare in Australia since a lone gunman killed 35 people in the tourist town of Port Arthur in 1996.

The Port Arthur Massacre sparked a world-leading crackdown that included a gun buyback scheme and limits on semi-automatic weapons.

But many Australians are now questioning whether those laws are equipped to deal with online sales and a steady rise in privately owned guns. 

"This horrific situation now, it does make me personally feel that they need to be stricter," David Sovyer, 43, told AFP.

Retiree Allan McRae, 75, said "not a lot of people need a gun".

"It would've reduced the possibility of it happening if more people had reduced access to a gun," he told AFP.

The attack has also revived allegations that Australia is dragging its feet in the fight against antisemitism.

"The last four years, I was very clear. And I was very clear about the dangers of the rise in antisemitism," Israel's ambassador to Australia, Amir Maimon, said while visiting a memorial to the victims on Tuesday. 

Australian Jewish Association head Robert Gregory told AFP the government had "failed to take adequate actions to protect the Jewish community".

Israeli Prime Minister Benjamin Netanyahu said Australia's decision to recognize Palestinian statehood this year had poured "oil on the fire of antisemitism". 

Desperate to help, Australians have lined up in their thousands to donate blood to the wounded. 

Red Cross Australia said more than 7,000 people had given blood on Monday, smashing the previous national record.

A makeshift flower memorial next to Bondi Beach swelled in size on Monday evening as mourners gathered to pay tribute to the victims and mark the second day of Hanukkah.

Hundreds of mourners, including members of the Jewish community, sang songs, clapped and held each other.

Leading a ceremony to light a menorah, a rabbi told the crowd: "The only strength we have is if we bring light into the world."

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