Richard Tutt, head of Magna Academy in Poole, told the BBC the technique would only be used in cases where pupils are on the verge of permanent exclusion.
It was part of a much wider system, he said, where pupils are rewarded with points which they can use to buy items.
But some parents accused the school of humiliating or bullying pupils.
Mr Tutt, who took over the secondary modern four years ago, said his students were rewarded far more than they were punished.
"This needs to be taken in a far wider context. We have a very well established behaviour sanction and reward system," he said, adding that behaviour was impeccable at the academy.
This included an online reward system, where students received points for good behaviour, which could be used to buy things like nail manicures or footballs.
Pupils at the school, 40% of whom are classed as disadvantaged, are also rewarded with free coffees or by being allowed to go to the front of the lunch queue, Mr Tutt said, as well as usual status positions, such as being made prefects.
One Facebook post, from Jodi Taylor, said: "My god-daughter goes to this school and this is just a few of the things they threaten.
"She is frightened to go to school and she is a good girl. It is nothing short of bullying, the good kids are being treated as bad and been threatened on a daily basis.
"School is meant to be a fun part of growing up?"
A parent, also writing on Facebook, said that the idea was an "absolute disgrace", adding: "My boys go to this school. If they try that with my boys I will seek legal action."
Mr Tutt said the assembly apology sanction was reserved for extreme cases and had not yet been used.
"It is to deal with repeat offenders who have received fixed term exclusions. The type of behaviour being punished might include being in complete defiance of a teacher or physical violence.
"And bear in mind we are a school in a challenging environment and we want them to learn."
He said there had been a very small minority of parents who did not sign up to the idea.
A letter to parents said: "Any student whose behaviour disrupts the learning of others will be expected to stand up at the front in their faculty assembly, face their peers, and apologise to the whole faculty for letting them down.
It also says: "As from now, if any student receives a repeat fixed term external exclusion then, as part of our reintegration process, their parent(s)/carer(s) will be expected to sit next to them in lessons and to supervise them at break and lunchtime, for the day following the exclusion.
"This will help students, whose poor behaviour has caused them to be excluded, settle back into lessons and academy life."
Mr Tutt said students at risk of being excluded were offered a range of support and given pastoral care, because the school did everything it could to avoid permanent exclusions.
The school was in the top 7% of for academic progress across eight GCSEs in England during the 2015/16 academic year.
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The principal of a Dorset academy which is planning to require poorly behaved pupils to apologise to classmates in assembly has defended the policy.