In a statement, he said the teenagers will face disciplinary action.
"There is no place for incidents like this at our school," Mr Anestis said.
"It is disappointing and does not reflect the behaviour of the overwhelming majority of our students."
He said the school immediately contacted emergency services, with police and ambulance officers attending.
"Neither student was seriously injured, and one was taken to hospital as a precautionary measure and has since been released," Mr Anestis said.
Footage of the fight shows the girls in the schoolyard wrestling, punching and kicking each other.
The video shows a crowd of students standing back watching the fight, some of whom are cheering.
One girl then starts choking the other who falls to the ground apparently unconscious.
Several students then run to her aid.
A woman claiming to be the mother of the girl involved who was not taken to hospital said her daughter had been a victim of bullying and was defending herself.
"It’s not quite as clear-cut as the video shows," she told 3AW radio host Neil Mitchell.
"There’s a king punch to the back of the head that’s not even on the video."
The mother said her daughter had recently left another school to escape bullying, but it had continued at her new school.
“[My daughter is] very, very bruised and very sore,” she said. “She’s black and blue as well.
“As a parent I’m disgusted, I’m appalled. I’m just horrified to actually watch. I’m mortified."
Police said the girls and their parents had been spoken to and the investigation was ongoing.
News of the incident comes on the same day the state government announced $8.9 million funding boost for public schools to combat an increase in violence and aggression on school grounds.
The ''protective schools package'' will see the establishment of a new operations centre and reporting system, as well as extra training for principals, teachers and support staff.
The number of minor assaults or aggressive behaviour reported to the Department of Education rose from 1179 in 2016 to 1613 in 2017, although the number of serious incidents declined.
Education Minister James Merlino said the spike was directly related to new reporting requirements and an increased focus on the issue.
He said he hoped early intervention, rather than strict disciplinary action like expulsion, would put an end to violence in schools.
"We have zero tolerance for violence and aggression in schools," he said. "But simply moving the child on doesn't fix the problem."
with AAP
Anna is a breaking and general news reporter at The Age.
Melissa Cunningham reports breaking news for The Age.
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