Australian law enforcement and intelligence agencies are to be reviewed, in the Albanese government’s latest response in the wake of the Bondi tragedy.

But Prime Minister Anthony Albanese is still resisting calls for a national royal commission.

Albanese said in a statement after a meeting of cabinet’s national security committee that the review would be done by the Department of Prime Minister and Cabinet. It will be led by Dennis Richardson, a former secretary of the defence and foreign affairs departments, as well as a former head of ASIO.

There have been questions about the adequacy of ASIO’s performance. It checked out Naveed Akram – the younger of the father and son gunmen – in 2019, because of his radical contacts, but did not later keep tabs on him.

Albanese said the review would “examine whether federal law enforcement and intelligence agencies have the right powers, structures, processes and sharing arrangements in place to keep Australians safe in the wake of the horrific antisemitic Bondi Beach terrorist attack”.

But critics inside and outside the Jewish community, including former treasurer Josh Frydenberg and former prime minister Scott Morrison, say the review is an inadequate response and continue to call for a federal royal commission.

New South Wales intends to have one. Premier Chris Minns said at the weekend: “We need a comprehensive look at this horrible terrorism event. Right now, we’ve got bits and pieces of the jigsaw puzzle, but until we’ve got a full and accurate picture of how this happened with a plan to ensure it doesn’t happen again, then I don’t have the answers to the people of NSW about what happened on Sunday.”

Albanese said he would support whatever NSW did but has pushed back on the calls to establish a royal commission himself, claiming it would slow responses to the tragedy.

Frydenberg, a leader in the Jewish community, said the review was a weak response. He said it “will not go to the heart of the issues and the radicalisation within our country”.

“Prime Minister what are you afraid a Commonwealth Royal Commission will uncover?” Frydenberg said.

“The Commonwealth must take the lead with the most comprehensive, powerful Royal Commission possible. You supported Royal Commissions into the banks, veterans, aged care and welfare system.

"Now 15 innocent souls including 10 year old Matilda have been murdered by radical Islamists and all you are prepared to commit to is an internal departmental review? It beggars belief and is the latest failure in federal leadership.

"It’s not good enough to pass the buck to NSW whose Premier has already indicated he will hold a Royal Commission. Why is a Royal Commisson good enough for NSW but not the Federal Government?

"The threat is national,” Frydenberg said.

The prime minister said in his statement: “The ISIS-inspired atrocity last Sunday reinforces the rapidly changing security environment in our nation. Our security agencies must be in the best position to respond.” The review will be finished by the end of April and made public.

Both Minns and Albanese said anti-immigration rallies organased for Sunday – designated as a day of reflection for the Bondi victims – should not go ahead and urged people not to attend them. Barnaby Joyce, now with One Nation, addressed the Sydney rally.