The lawyer of a man shot and killed by police has called on authorities to release evidence that he was an Islamic State sympathiser, saying the police PR machine has gone into overdrive.

Raghe Abdi, 22, reportedly yelled "Allahu Akbar" and lunged at police with a knife when he was shot alongside the Logan Motorway in Brisbane on Thursday.

Police say they are investigating whether he is linked to the alleged murder of an elderly couple in a nearby suburb.

Mr Abdi had been linked to IS after being arrested by counter-terrorism police at Brisbane Airport about three months ago and subsequently released on bail.

Mr Adbi's lawyer and president of the Australian Council of Civil Liberties, Terry O'Gorman, told NewsWire there was no substantiated evidence that he was an IS sympathiser when he fronted court.

He said claims made in The Courier-Mail that bodycam footage showed Mr Abdi yelling "Allahu Akbar", Arabic for God is Great, should be released.

"The was absolutely no evidence put forward about the allegations (that he was an IS sympathiser) in court," Mr O'Gorman told NCA NewsWire.

"The only evidence was that one person claimed that he said he had some sympathy for ISIS.

"There is no other evidence to back up that assertion and that person was never cross-examined.

"If the police are claiming he said that then the evidence should be produced, otherwise it's simply not credible."

He said police were renowned for releasing information after a shooting that the person was known to police.

"It's a typical a police tactic when they shoot and kill someone, their police PR machine goes into overdrive to put that person in the worst possible light," he said.

"If there is hard information to that effect (an IS sympathiser), well fair enough for the comment to be made, but it is made on the comment of what he said to one person, and he denied that in his instructions to me that he said that."

The shooting was about nine hours before police made a welfare check and found an 87-year-old man and an 86-year-old woman dead at a Parkinson home. They had suffered significant injuries.

Police are now investigating whether the alleged murder of the man and woman at Parkinson is linked to the fatal shooting of a man at Drewvale on Thursday morning.

Police said the investigation was at an early stage and no further information could be confirmed at this time.

The Ethical Standards Command is investigating the police shooting, which will be overseen by the Crime and Corruption Commission.

Originally published as Dead man's lawyer to cops: 'Prove he yelled Allahu Akbar'