Fergus Linehan, who will leave the role after the 75th-anniversary season of both events in August, said the city’s festivals should “welcome scrutiny”.
And he said it it was right for “unfair or illegal” practices to be highlighted where they are uncovered.
However, he suggested it was unfair and unhelpful for the whole Fringe to be criticised.
And he defended the DIY nature of the Fringe, which has famously embraced an “open access” ethos since it was instigated in 1947 by theatre companies who found themselves excluded from the first International Festival.
However, Mr Linehan said there was a clear distinction between genuine volunteer initiatives and roles which were “painted as volunteer work”.
He said people involved with the festivals had to "guard against any sense of exploitation of enthusiasm andambition".
Mr Linehan has spoken out weeks after independent research called for the Fringe Society to shelve the event’s “open access” principle and instead put in place official standards or “best practice” guidelines for the first time.
Fringe Society chief executive Shona McCarthy has since announced “core principles”, which venues would be asked to sign up to, would be published in the summer as part of a new blueprint for the future of Fringe.
She has insisted there is “absolutely no place at the Fringe for exploitation”, but has defended the different financial models used by venues, including those run entirely by volunteers.
Mr Linehan said: “I think we’ve got to be really specific about this. Talking about ‘the Fringe’ is slightly meaningless.
“We need to talk about it in terms of the specific entities that are employing people on a voluntary basis and they are clearly working beyond what is legally described as volunteering.
“People have to guard against any sense of exploitation of the enthusiasm and ambition of people to have some kind of platform.
"But volunteering is one of the great success stories of Scotland – the volunteer sector is amazing.
"I don’t think people should be exploited and I don’t think people should be doing work that isn’t volunteer work and is painted as volunteer work, but we have to get into specifics. That is happening now.”
Some of the biggest venues at the Fringe have come under fire from union leaders and campaigners over their use of volunteers and rates of pay.
Mr Linehan added: “Sometimes there are things you can do within a volunteering context where no-one makes money at the other end of it. Sometimes a bunch of people form a theatre company and do everything together.
"A lot of this relates to the way a company is constituted and what everyone is getting.
“Generalising about the Fringe doesn’t work. But I think what does is saying ‘are there practices that are unfair or illegal?’, getting to them and pointing them out.
"Edinburgh is an exceptional circumstance. People look at the commercial heft of what happens here in August. We should all welcome scrutiny.”