In his most robust defence yet of why a security agency review was more appropriate, the prime minister said he did not want to politicise a moment of national grief.
"My job as the leader, as the Prime Minister, is to bring the country together, not to seek to divide, not to seek differentiation, but to seek common interest," he said in Canberra on Tuesday.
"What we should do is go to the heart of what occurred and importantly, how do we make sure that this never happens again."
Mr Albanese hinted at several failures under the former coalition government, such as letting Sajid Akram, 50, one of the gunmen who was killed by police, come to Australia on a student visa in 1998 before he was granted a partner visa in 2001 followed by a NSW gun licence.
But he quickly noted that "all of these issues we should not play politics with."
The prime minister has so far resisted calls for a national royal commission on the Bondi Beach attack, when 15 people were killed at a Hanukkah event, in favour of a quicker and "safer" independent review process.
Retired intelligence head and former diplomat Dennis Richardson will lead the review, which will examine the actions of Australia's federal law enforcement and intelligence agencies leading up to the Bondi attack on December 14 that ended with 15 dead.
But the families of those killed and Jewish groups have criticised the review process as an "ineffective half measure."
Mr Albanese said he understood their calls came from "a good place."
"This atrocity is something which, understandably, people want answers on how it occurred. I want answers too and I want justice done," he added.
Home Affairs Minister Tony Burke said the review was the best way forward due to the experience Mr Richardson brings to the table, and because a royal commission could take years.
"You don't get anyone better than a national security expert who has lived his life making these sorts of assessments, rather than somebody who is learning it in the course of an inquiry," he said at a press conference alongside Mr Albanese.
The review report is due by the end of April.
But others have argued a royal commission could offer an interim report to provide answers sooner on the shooting, which involved a father and son duo who were allegedly influenced by Islamic State, or ISIS, ideology.
Executive Council of Australian Jewry co-chief Alex Ryvchin said the government's response was insulting and described the review process as an "ineffective half-measure".
Former federal Liberal treasurer Josh Frydenberg, who is Jewish, continued his attack on the government, saying its argument that a royal commission risked further fraying social cohesion was disingenuous.
"The argument ... that it would platform the worst voices is akin to saying the Nuremberg trials shouldn't have been held because you don't want to platform Nazi propaganda," he told Sydney radio 2GB Radio on Tuesday.
Monash University public policy expert Deirdre O'Neill said she understood why many in the Jewish community felt let down.
"They're looking for answers and their sense is that they won't get it from a review," she told AAP.
But Ms O'Neill said her research on policy change showed it was not necessarily true that one form of inquiry was better than another.
"The thing about royal commissions is that they're seen as the highest possible form of independent inquiry," she said.
"But there are a lot of people who would argue that royal commissions aren't that effective."
Although royal commissions can subpoena witnesses and make recommendations, they can't implement findings and their success often depends on many factors.
These include the terms of reference used, clear definitions of the problem at hand, recommendations that can work in the real world and resources and time available.
NSW Premier Chris Minns has already committed to a state-based royal commission, which Mr Albanese supports.
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