Australian Prime Minister Anthony Albanese showed his support on Tuesday for a proposed national firearm register in the wake of a deadly police shooting.

Albanese said his government would take advice from law enforcement on how information can be better shared to protect police officers and the general public from firearms, flagging discussions as a priority when he next meets with state and territory leaders at the national cabinet.

"I am certainly up for dialogue with the states and territories about how there can be a better national consistency and national information that can serve the interests of police going about their duty," he said.

A public memorial service was held on Wednesday in Brisbane for Constables Rachel McCrow, 29, and Matthew Arnold, 26. The two were shot dead when they were ambushed by Gareth Train, his brother Nathaniel and wife Stacey at a remote property approximately 300 kilometers west of Brisbane while carrying out a missing persons inquiry on December 12.

Fellow officer Constable Randall Kirk was shot and injured while Constable Keely Brough hid in nearby bushland before escaping.

Neighbor Alan Dare, 58, was also killed by the Trains, who all died when police stormed the property.

In the wake of the shooting, police unions across the country have called for the establishment of a national gun owner's register, which was first recommended in 1996.

Currently, police cannot readily access information about whether a person holds a gun license in another state as was the case with Nathaniel Train in New South Wales.

The Police Federation of Australia has also called for mental health checks to be conducted to obtain or renew a gun license.