The Tonga Secondary Schools' Principals Association says cancelling future rugby matches will not stop violence between supporters.
Ex-students at a senior rugby game between Liahona High School and Apifo'ou College started a brawl in the weekend cutting the match short.
The police and the principals' association will meet this week to decide if the rest of the season should be cancelled.
The association's president, Aisake Vaisima, says violence often accompanies sports events and the students are paying the price for other people's poor behaviour.
"The athletes are very sad when these things happen because their competitions will be cancelled or stopped all together. As I see it, it's not their intention to go in and fight, the perpetuators are students who have left school."
Aisake Vaisima says the principals need to work on strengthening inter-school relationships to reduce future conflicts.