Labor Senator Helen Polley and Greens Senator Nick McKim both said a national discussion was needed around gun control, a sentiment also supported by the Tasmanian Liberal government earlier this week.

In comments made on Wednesday, Senator Polley said she would support a national firearm registry, citing a sense of "frustration" around a lack of action since the Port Arthur Massacre in 1996.

"How many more incidences do we have to live through before action is taken," she said.

"We know there's too many illegal firearms coming into this country, so at least we want to know who's doing the right thing and registering those firearms - the public have a right to know."

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Senator McKim said the Greens would "strongly support" a national firearms registry to address inconsistencies in gun laws between different states.

"For decades the Greens have been proud to lead the debate on gun control," Senator McKim said. "All too often we are tragically reminded that we cannot become complacent when it comes to firearm control."

The groundswell of support has also found the ear of prime minister Anthony Albanese, who on Tuesday flagged discussions around ways to improve coordination of information about guns at the next national cabinet.

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Queensland Premier Annastacia Palaszczuk last week said she would raise the issue at national cabinet after police were killed at a remote property in Wieambilla. Western Australia Premier Mark McGowan also voiced his support over the proposal.

A national firearms register was first recommended following the Hoddle and Queen street massacres in the 1980s.

If implemented, the registry would replace the Australian Firearm Information Network.

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