Edinburgh Academy rector Marco Longmore said yesterday it was 'extremely regrettable' that the behaviour of a small number of pupils fell below the school's standards.
A comprehensive review has now been ordered to ensure high standards at all future camps and school activities.
The comments came as a police inquiry gets under way into claims at least four cadets were put inside sleeping bags and whipped with wire coat hangers while on a trip in Aberdeen.
Parents reported that the youngsters returned from the Easter trip covered in bruises.
Mr Longmore said: "We have carried out a thorough and detailed investigation of the incident at the recent Easter Combined Cadet Force [CCF] camp.
"It is extremely regrettable that the behaviour of a small number of pupils fell far below that expected by the school.
"It is a clear signal of how seriously we have viewed this behaviour that we sanctioned four pupils to the maximum level of the school's ability, short of complete expulsion.
"In addition, four other senior pupils who attended the Easter camp have been instructed not to attend CCF activities."
Mr Longmore said the suspended pupils had been "extremely chastened" but that they have been appropriately punished and will be allowed to return to the school.
He said the school had made strenuous efforts to ensure high standards at the CCF camp and that clear and 'unambiguous' instructions were given to all participants beforehand. However, he added there are 'lessons to be learned.' and senior staff would now be taking out a comprehensive review of procedures for all future activities.
Police Scotland are in the early stages of an inquiry into the incident after being called in by the school. A spokesman said: "Police in Edinburgh are investigating following assaults on pupils from a school within the capital.
However, a source at the £11,000 a year school said the incident raised serious questions about pupil supervision on trips away. The insider added: Why weren't the teachers aware of what was going on? And if the were, why didn't they report it?
"These parents pay a lot of money to send their children to a top school and they deserve to find out exactly what happened on that trip in terms of both pupil behaviour and teacher supervision."
The school's website describes the camp as a "is a self-run Adventurous Training/Military camp ".