The Turnbull Government is debating how it should tackle radicalisation in the wake of Friday's fatal shooting in Sydney.

Some public servants and Coalition frontbenchers think the Countering Violent Extremism program is failing and alienating Islamic community leaders.

They say it is badly named and ill-suited to being part of the national security portfolio, inside the Attorney-General's Department, and want it rebranded under a "social cohesion banner".

There is a push for it to be moved into multicultural affairs, in the belief that will allow the Government to "do more heavy lifting at the soft end" of the counter-terrorism fight.

Only a small proportion of the $13.4 million allocated to the program has been spent and there have been inter-agency complaints about the capacities and responsiveness of those running it.

Several Islamic leaders and other community groups have told the Government they are reluctant to face the social stigma associated with accepting money explicitly intended to stop terrorism.

Ministers are also considering "softer" ways of getting friends, families and teachers to report or reach out to young people at risk of becoming radicalised.

Yesterday, Assistant Minister for Multicultural Affairs Concetta Fierravanti-Wells said she thought parents were highly unlikely to dob in their children to a national security hotline, a move that instantly attracts the attention of security agencies like ASIO and the AFP.

"Involvement with Daesh [Islamic State] is now what is being termed to me as a new way to rebel," she said.

"We need to ensure we have avenues open for those people to seek help but not necessarily just in the national security arena."

Justice Minister Michael Keenan, who currently oversees the Countering Violence Extremism program, defended it today.

Any push to remove the program from his portfolio is likely to face a fight.

"We have been very keen to make sure the community is working with the Government," Mr Keenan said.

"It is a big challenge but we are doing everything we can to meet that challenge."

Some of the Government's recent anti-radicalisation efforts have had teachers and green groups up in arms.

They were upset by a 32-page booklet which linked environmental activism and alternative music with violent radicalisation.