Australia’s Labor opposition has used the anniversary of the Christchurch massacre to call for a review of the criteria used to judge terrorist organisations, citing the fact no rightwing extremist groups are listed in Australia.

The shadow home affairs minister, Kristina Keneally, has proposed the Morrison government allow the parliamentary joint committee on intelligence and security to review the criteria to ensure they are fit for purpose.

The massacre of 49 people at two mosques in Christchurch in March 2019 prompted calls for greater social cohesion in Australia and a renewed focus on extreme rightwing terrorism, particularly by the Labor party.

In October Australia’s spy agency warned extreme rightwing terrorism had become “more cohesive and organised” – a warning repeated in February. The home affairs minister, Peter Dutton, was soon after criticised for promoting a false equivalence between radical far-right groups and “leftwing terrorism”.

The United States and Britain have listed extreme rightwing groups as terrorist organisations. Dutton has said he will do the same if the Australian Security and Intelligence Organisation recommends it.

Listing an organisation on the terrorism list criminalises membership or association with the group.

Keneally has told Nine newspapers that Asio’s warnings about rightwing extremists seemed inconsistent with the fact no rightwing groups were on the terrorist list.

“It may be that the criteria for listing organisations in Australia isn’t fit-for-purpose when it comes to rightwing extremism,” Keneally reportedly said.

“For example, the definition of terrorism in Australia and the UK is similar but with a stark difference: the UK definition of terrorism explicitly extends to violent acts or threats made for the purpose of advancing a racial cause.

“The Australian government and all federal parliamentarians must now take the terrorist threat of rightwing extremism seriously and respond.”

Keneally suggested the joint committee could review the criteria for listing terrorist organisations, a bipartisan move that would ensure parliamentarians don’t “play politics or engage in culture wars over such issues”. “Keeping Australians safe is too important for that.”

In a statement on Sunday the prime minister, Scott Morrison, said Australia “stands in unity and solidarity with New Zealand on the first anniversary of the horrific terrorist attacks in Christchurch”.

“New Zealanders responded to hate with love in the aftermath of this terrible incident, and that powerful message endures today,” he said.

“Our two nations share an ongoing commitment to peace and freedom and we continue to reject those who seek to spread division and hatred.

“Globally, whether it’s the Christchurch Call to Action or last year’s G20 and G7 resolutions to stamp out online hate and violence, New Zealand and Australia will continue our work to ensure something like this does not happen again.”

In April Australia passed world-first legislation to crack down on violent videos on social media, to prevent a reoccurrence of the Christchurch attacker’s video spreading on social media faster than it could be removed.

In February Guardian Australia revealed that one of Dutton’s staff members cited the climate activist group Extinction Rebellion as an example of a troublesome leftwing organisation during a telephone conversation with a member of the public who sought to query his claims leftwing groups also posed a risk.