According to reports, the two 15-year-old boys at the centre of the incident are pupils at a high school in the Limassol district.
The police were called in to separate the boys but not before one was left with eye injuries and the other with injuries to his leg.
Police also found an axe and a piece of wood at the scene.
Investigations into the circumstances surrounding the incident are continuing.
The new fight came the day after an incident involving a group of 14-year-old girls at a Nicosia school .
Teachers intervened in time to prevent one of the girls from approaching another with a kitchen knife, but not in time to prevent one of the girls being thrown to the ground and hit by the others.