Australian authorities are investigating the extremist views of three people who shot and killed two officers and a neighbour at a rural property before they were killed hours later by police in a gunfight.

Investigators will look at the possible extremist links of the killers after a series of posts under the name of Gareth Train, one of the murderers identified in the wake of Monday’s deadly shootout, were found on conspiracy theory forums, Queensland Police Commissioner Katarina Carroll said late on Tuesday.

The posts include references to anti-vaccine sentiments and claims other high-profile shootings were hoaxes or false-flag operations.

“It’s very difficult at the moment for us to reason with what has happened. There are no obvious reasons,” Ms Carroll told the Australian Broadcasting Corp.

But she said she has no doubt that over the coming days and weeks, police will come back with some insight into the tragic events which unfolded.

Research and surveys show belief in conspiracy theories is common and widespread.

Believers are more likely to to get their information from social media than professional news organisations. The rise and fall of particular conspiracy theories are often linked to real-world events and social, economic or technological change.

Ms Carroll said every possible motive for the killings is being examined, including whether it was a premeditated attack on the officers.

“Some of the stuff that’s online from these people, we will investigate what they have been doing not only in recent weeks but in recent years, who they’ve been interacting with,” she said.

Four officers arrived at the property in the town of Wieambilla, in Queensland state, to investigate reports of a missing person. They walked into a hail of gunfire, Ms Carroll said, and it was a miracle two officers managed to escape and raise the alarm.

Those killed were Pcs Matthew Arnold, 26, and Rachel McCrow, 29, along with 58-year-old neighbour Alan Dare.

One of the officers who escaped, Pc Randall Kirk, 28, was recovering at a hospital from shrapnel wounds on Wednesday. He said he and his wife wanted to thank everybody “from the Prime Minister down” for their messages of support.

“I’m feeling fine, just a little sore. My main thoughts are with the other police families at this awful time,” Mr Kirk said in a statement released by the police union.

“It means a lot to know the community cares for us all.”

Prime Minister Anthony Albanese earlier told reporters in Sydney the country is mourning with those affected.

“This is, indeed, a devastating day for everyone who loved these Australians, and our hearts go out to those in the grip of terrible grief,” he said.

“We know that this news has fallen hard on a close-knit and caring Queensland community. As well as, of course, the community to which all police officers belong.”

He said officers across the nation know the risks they face, yet do their duty.

“And today and every day I pay tribute to each and every one of the police officers who serve their local communities and who serve their nation,” Mr Albanese said.

“This is not a price that anyone who puts on the uniform should ever pay.”

In all, six people died in the violence on Monday in Queensland state.

The killers have been identified as former school headteacher Nathaniel Train, 47, his brother Gareth, 46, and sister-in-law Stacey, 45.