Prime Minister Anthony Albanese on Thursday announced a royal commission after weeks of intense lobbying from Jewish groups, business leaders, the opposition and others.
Former High Court judge Virginia Bell will lead the inquiry, examining the nature and prevalence of anti-Semitism and religiously motivated extremism, and will report back by the one-year anniversary of the attack.
Opposition Leader Sussan Ley said the royal commission needed to examine the decision making within the government.
"Ministers (need to) be called to account," she told ABC TV on Friday.
"The executive of government needs to answer - effectively in the dock - what warnings were given, what warnings were ignored, what action was taken or maybe not taken.
"If Anthony Albanese had been as determined to tackle anti-Semitism over the last three years as he was to avoid this royal commission over the last three weeks, I think we would be in a better position today."
The prime minister said the decision on who would testify at the inquiry would be left with the royal commissioner.
Calls for the fully-blown national probe have dramatically escalated over the last fortnight.
Mr Albanese initially preferred an independent inquiry led by former ASIO boss Dennis Richardson, insisting this was recommended by "the actual experts".
On Friday morning he said the royal commission was announced "in record time", with the previous days spent listening to communities.
"The last funeral was just two days ago, and so I have listened. We've made sure that we've got it right as well," he told Seven's Sunrise.
"We needed to get the right commissioner, the right terms of reference in the right time frame, because we can't afford to not get this right. It's essential for bringing the nation together in national unity and building social cohesion."
The choice of Ms Bell as commissioner had prompted disquiet among some members of the Jewish community because of her previous rulings on protest laws.
Among those to query the choice was former federal treasurer Josh Frydenberg, previously the coalition's most senior Jewish MP.
On Friday morning, Mr Frydenberg said Ms Bell would be supported as the royal commission "needed to be successful".
"Now that Virginia Bell has been appointed, the Jewish community will get behind her, provide all the evidence, provide the testimony, in order to get the best recommendations, the most practical road map to take our country forward," he told ABC TV.
"The Jewish community wants to have trust and confidence in the person at the helm of this royal commission. That's the most important thing.
"We're all heavily invested in making this royal commission a success."
University of New South Wales associate law and justice professor Harry Hobbs said there had been more than 140 royal commissions in Australia's history, and the research was clear about what kinds of recommendations were most likely to be implemented.
"Generally speaking, you want recommendations that are practical and affordable and simple ... because those things are more likely to be accepted," he told AAP.
"If they are complex and costly and difficult and contested, then they are less likely to be implemented."
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