A 16-year-old boy was killed in a Reservoir street about 2.15am on Sunday, while a 23-year-old man was fatally stabbed in Docklands about an hour later.
A 26-year-old man, the 23-year-old's brother, was also taken to hospital after the Docklands attack. He remains in a serious but stable condition.
Detective Superintendent Paul O'Halloran described the Reservoir stabbing as vicious, saying the boy was chased by a group before being repeatedly stabbed in a suspected targeted attack.
He said a group of males set upon the other two victims at Docklands after an earlier altercation.
Det Supt O'Halloran said police believed the two incidents were not linked to each other or Melbourne's Moomba festival.
No one has been charged over either fatal stabbing
Det Supt O'Halloran said the violence was unacceptable.
"Any dispute, whatever it is, will never justify people being attacked with knives and people certainly losing their lives," he said on Monday. "That's just tragic.
"We all must understand as a community that we can have our differences but there certainly shouldn't be any other knife fights."
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