Three people have died, including one man shot by police, with a fourth person taken to hospital in a critical condition after what investigators believe is a random stabbing spree across Melbourne's east.

Key points: Police said the man's mental health had been flagged in the force's internal database, but he had no criminal history

Police said the man's mental health had been flagged in the force's internal database, but he had no criminal history He was shot dead after police tried to arrest him after midnight

He was shot dead after police tried to arrest him after midnight Investigators do not believe the victims were known to each other or to the killer

Police believe the man stabbed a Protective Services Officer (PSO) at a train station near the MCG, caught a train to the neighbouring suburb of Hawthorn where he killed one woman and left another with life-threatening injuries, then stabbed another man in Kew who later died from his wounds.

Officers then shot the suspected killer dead while attempting to arrest him on a nearby street.

Victoria Police Chief Commissioner Graham Ashton said the suspected killer, a 34-year-old Roxburgh Park man, had visited police stations twice in 2018 because he believed "ISIS operatives from Mildura have been out to kill him".

Commissioner Ashton said the police had flagged his mental health in the internal crimes database LEAP (Law Enforcement Assistance Program).

An investigation into the deadly attacks has so far not found any links to terrorism.

Emergency services remained at the crime scene at Cotham Road in Kew on Thursday morning. ( ABC News: Leanne Wong )

Investigators said there was nothing to suggest the victims were known to the man.

"There's nothing to indicate at this early stage that this is anything other than a random act of senseless violence," Assistant Commissioner Glenn Weir said on Thursday morning.

No apparent motive for attacks

Police raided the man's Roxburgh Park home as they searched for a motive for the deadly attacks.

Commissioner Ashton said the man was not taken in for assessment after either of the two conversations with police in 2018 about his fears about "ISIS operatives" and was not under active surveillance.

He said the man had no criminal history, no warrants out against him and no parole history.

Police found the suspected killer on Walton Street in Kew. ( ABC News )

He had an intervention order out against him by his estranged partner and child, but Commissioner Ashton said he had not breached the order in the years it had been in place.

"To go from so little background to the offending he had last night, that's unusual," he said.

He said investigators were "eagerly awaiting toxicology results".

PSO to undergo plastic surgery after train station stabbing

Police said the first attack happened at Jolimont Station, near the MCG, about 10:40pm on Wednesday night.

Commissioner Ashton said the man was speaking to two PSOs when he pulled out a large knife "without any warning" and slashed one of the officers across the cheek and arm.

He then fled the scene on foot.

The PSO was treated in hospital after being assaulted at Jolimont Station. ( ABC News )

PSOs are uniformed members of protective services who monitor trains, stations and surrounding areas.

The officer will undergo plastic surgery on his cheek and is recovering in hospital.

Women attacked returning home in Hawthorn

Police said it was believed the man fled past the MCG to nearby Richmond Station, where he then caught a train to Glenferrie Station in Hawthorn.

Investigators remained at the Coppin Grove crime scene throughout the morning. ( ABC News: Simon Tucci )

He travelled to Coppin Grove, where two women were returning home in their car after a night out about 11:20pm.

He attacked the women after what police said was a short conversation.

A 30-year-old woman died at the scene.

Her 31-year-old companion was taken to the Alfred Hospital, where she is now in a stable condition.

"It's just a random, dreadfully wrong place at the wrong time," Commissioner Ashton said.

It is believed neighbours called emergency services after hearing screaming, but there were no witnesses to the attack.

Victim called police after Kew attack

Police said the man then travelled to the neighbouring suburb of Kew, when he stabbed another victim who was out for a walk.

The 59-year-old man called triple zero and the Police Communications Centre as he lay bleeding.

"He's made that call because obviously he's worrying about the community more than himself," Commissioner Ashton said.

"He's worrying about what else this guy's going to do and who else he's going to harm. So I think it's a tremendously brave act," he said.

Police have set up a number of crime scenes across Melbourne's inner east. ( ABC News )

Police found him with critical injuries near Cotham Road and Queen Street about 12:15am.

Officers gave the man CPR and called an ambulance, but the 59-year-old died shortly afterwards in hospital.

Suspected killer shot dead after coming at officers

A large police operation, including Critical Incident Response Team (CIRT) officers, found the suspected killer a short time later on Walton Street in Kew.

He came at CIRT members with a knife with "in their view, lethal intent", Commissioner Ashton said.

After trying to subdue the man using tasers and non-lethal bean bag rounds, police shot the offender.

He died from his gunshot wounds at the scene.

"I heard somebody shouting out 'drop the knife, drop the knife, drop the knife it's on your head' and then bang, bang, bang," Kew resident Peter Walker said.

"After the bangs, silence. Absolute silence. No more running, no more calling out, no more gunshots.

"The police gave plenty of warning, they did a very good job."

Commissioner Ashton said he was found with two large kitchen knives and a smaller portable knife.

Police Minister Lisa Neville praised the officers for their "quick actions".

Crime Command, the Homicide Squad and Armed Crime are leading the investigation.

The investigation will be overseen by Professional Standards Command, which is the protocol any time police fire a gun, and the coroner.

Anyone with information is asked to contact Crime Stoppers.