A desperate search is under way for Peter O'Ryan, 48, whose last known location was his family's home in the Gippsland town of Tyers.
He is alleged to have entered the Cowies Road property about 12.30pm on Saturday before attacking his brother and turning on his mother and father.
The alleged attack, which Victoria Police Detective Senior Sergeant Rodney Findlay said was among the worst he had seen, is believed to have followed an argument.
"I've been working in family violence a long time," Det Sen Sgt Findlay told reporters on Sunday.
"This is some of the most serious offending I've ever seen."
O'Ryan's father and brother, aged 77 and 47, were airlifted to hospital with life-threatening injuries and remain in critical condition.
His mother, aged 74, was transported to hospital with critical injuries and remains in a stable condition.
Police said they conducted a widespread search for O'Ryan, who was alleged to have fled the scene on foot and was likely still armed.
"We are working furiously to try and bring him into custody so that we can make sure everyone's safe and he's held to account," Det Sen Sgt Findlay said.
Detectives are still working to establish the circumstances surrounding the incident, limited by the serious condition of O'Ryan's alleged victims.
His father and brother required immediate surgery and remained in intensive care at the Alfred Hospital. They have not regained consciousness.
His mother, meanwhile, has only been able to provide sparse details in between treatments, Det Sen Sgt Findlay said.
Police released images of O'Ryan on Sunday in the hope people would recognise him and provide information about his whereabouts.
O'Ryan was of no fixed address and was known to frequent the Morwell area, police said.
They said he had been known to take refuge in abandoned properties and outhouses.
Members of the public are cautioned not to approach him and to call triple zero if they see him.
Police have also directly appealed to O'Ryan to turn himself in, saying it would be in his and the public's best interests.
"Give yourself up, come and see us," Det Sen Sgt Findlay said.
O'Ryan was last seen wearing a black and mustard coloured jacket - visible in one of the images released by investigators - and carrying a black backpack.
He is Caucasian and described as being of medium build with dark grey hair.
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