Two brothers accused of a fatal assault outside a school during pick-up which left a man dead have had their charges upgraded to murder.

Liam Robert Harnett, 22, and Connor Edmund Harnett, 21, allegedly assaulted Andre Szep metres from Strathaird Primary School at Narre Warren South, in Melbourne's outer southeast, on June 12.

Police believe the attack occurred at a reserve near the school in the afternoon, shortly before students were due to leave for the day.

Mr Szep, 63, from Clyde North, was rushed to hospital in a critical condition, but died six days later.

The brothers were initially charged with recklessly cause serious injury, but on Wednesday, appearing separately via video link in Melbourne Magistrates Court, those charges were upgraded to murder.

Police believe the parties involved were known to each other.

The public prosecutor told the court detectives were still working through DNA and forensic evidence, which was expected to take three months, waiting on post-mortem results and additional physical evidence was still outstanding.

Several parents and students witnessed the incident and its aftermath, with one saying his priority was making sure his son was safe and did not become a witness to the event.

"I shielded my son straight away. I didn't want him to see anything," he said.

Jackie Mashiter had passed the reserve on her way to pick up her granddaughter from school when she saw a man on the ground surrounded by several people but did not initially realise what had happened.

"I just saw him laying down and I thought he was actually just resting and waiting for his kids to come out," she said.

The reserve is metres from the school grounds and a children's centre and is regularly used by families, dog walkers and local residents.

The brothers were remanded in custody and will next return to court for a committal mention on November 11.