Police were called to stop the fight, but turned back when the fight ended, Kings principal Dan Reddiex said.
A member of the public contacted the Otago Daily Times yesterday concerned there "was a lot of tension" between some of the schools' pupils.
There was general concern among some parents and teachers that escalation was "on the cards", because of some of the individuals involved, he said.
Mr Reddiex called a special assembly after Wednesday's schoolground fight.
"I told them there will be no retribution, because that is not the way we behave. This stops here. It goes no further."
However, he said he did not think tensions between the schools' pupils were heightened.
"I'm not too concerned. I know the boys from both schools and they are great boys. There has always been a rivalry between the schools, and I do want to maintain that, but in a healthy way, not in this way."
The school had informed the family of the victim, who was not injured badly in the fight, and it was now up to them if they wanted to take the matter any further, Mr Reddiex said.
Otago Boys rector Clive Rennie described Wednesday's incident as minor.
He said the boys involved had been spoken to and both schools were happy they had dealt with the matter appropriately.
"I don't believe it will go any further."
He reiterated Mr Reddiex's comments that there were no problems between groups from the schools.
The parent who yesterday contacted the ODT said he understood the pupil attacked on Wednesday had also been targeted by Otago Boys pupils about two weeks ago when travelling with other Kings pupils in a van along Portsmouth Dr.
The van was "nearly run off the road" and a fight ensued that resulted in the boy receiving a concussion which kept him off school for a week.
No emergency services were involved in that incident.
Neither principal was aware of the Portsmouth Dr incident.
The parent said Kings was a "great" school and he understood that much of what was going on was possibly happening outside of school, but he was concerned about both the targeted boy's safety and whether the situation would worsen if it was not dealt with.
"It would be a horrible situation if something serious did happen and everyone had quietly been talking about how bad it was getting."
