Naveed A. was shot by security forces during the attack and regained consciousness from a coma on Tuesday.
He and his father allegedly opened fire on crowds, killing 15 people and injuring dozens. Police killed his father during the attack.
"Early indications point to a terrorist attack inspired by ISIS," New South Wales state police said in a statement.
The alleged attackers spent most of last month in the southern Philippines, an area known for Islamist extremism. The Philippines said on Wednesday there was no evidence that the country was being used for "terrorist training".
According to authorities in Australia, the Philippines and India, the father was originally from India and held Australian residency, while the son was born in Australia
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Australia held the first funerals for the 15 victims who were killed in the country's worst mass shooting in almost three decades.
The first service was for Rabbi Eli Schlanger from the Chabad-Lubavitch of Bondi, who organized Sunday's Chanukah by the Sea event, where the attack occurred.
"After what happened, my biggest regret was — apart from, obviously, the obvious — I could have done more to tell Eli more often how much we love him, how much I love him, how much we appreciate everything that he does and how proud we are of him," said Schlanger's father-in-law, Rabbi Yehoram Ulman.
Ulman urged Jewish people not to fear visiting Bondi Beach or celebrating their faith despite the shootings.
He said the attackers want them to be afraid.
"But that is not the answer ... we can never ever allow them to not only succeed but any time they try something we become greater and stronger."
New South Wales health authorities said 21 injured people were still being treated in hospitals, five of them in critical condition.
The shooting shook Australia and intensified fears of rising antisemitism and extremism.
New South Wales Premier Chris Minns declared the attack a terrorist incident on Sunday evening. As a result, federal and state police launched a joint counterterrorism operation.
Minns said he will recall parliament next week to pass wide-ranging reforms of gun and protest laws.
"We've got a monumental task in front of us. It's huge," he said. "It's a huge responsibility to pull the community together. I think we need a summer of calm and togetherness, not division."
Australia's prime minister vowed to take whatever government action was needed to stamp out antisemitism.
"We will work with the Jewish community, we want to stamp out and eradicate antisemitism from our society," Albanese told reporters.
He agreed with the leaders of Australia's states and territories "to strengthen gun laws across the nation."
Editor's note: DW follows the German press code, which stresses the importance of protecting the privacy of suspected criminals or victims and obliges us to refrain from revealing full names in such cases.
