The man who stabbed to death two people and left a woman in critical condition before being shot dead by police in Melbourne had feared he was being hunted by ISIS.

Details of 34-year-old Mohammed Ibrahim's background have emerged as police continue their investigation into last night's killings as well as the man's attack on two Protective Service Officers.

Victoria Police Commissioner Graham Ashton said Ibrahim, from Roxburgh Park in Melbourne, had no links to terrorist organisations but in 2018 had visited two police stations to report an ISIS group based in Mildura was out to kill him.

Detectives had established the offender had no criminal record or bail condition but had two intervention orders taken out against him by his estranged partner and child. Both are safe and well.

Police have traced the dead suspect's movements after a night of violence left three dead and one person fighting for her life. (Nine)

Police say the "random act of senseless violence" appears to have started about 10.40pm.

The offender - who was carrying two large kitchen knives and a swtichblade - approached two PSOs at Jolimont rail station, near the MCG, asking for directions.

He slashed one across the cheek and arm before running from the scene and taking a train to Glenferrie station, near Hawthorn.

At about 11.15pm, he started talking with two women - aged 30 and 31 - getting out of their vehicle at Coppin Grove before stabbing them. The 30-year-old victim died at the scene.

(Nine)

Police are investigating if the violent incidents in Melbourne and have not yet ruled out terrorism as a motive. (Nine)

Paramedics called to the scene took her injured companion to hospital, where she is in critical condition.

Police were then called to reports of a man stabbed near a tram stop in Kew about 12.15am.

That man, 59, died in hospital, while the offender was spotted by police a few hundred metres away, in Walton Street.

Police officers at one of the crimes scenes in Melbourne after three people died overnight. (Nine)

Police had called on the suspect to surrender before he was shot.

Commissioner Ashton said detectives are continuing their investigations.

Meanwhile, roads and tram lines in the area are reopening after the incidents.

Cotham Road in Kew has been re-opened to traffic in both directions between High Street and Gellibrand Street.

Route 109 trams have resumed along their normal lines.

Delays may occur as Yarra Trams restore to normal frequency.

No citybound trains are stopping at Jolimont Station.