Fringe Society chief executive Shona McCarthy said she believed there was a "level of unease" and volatility among participants ahead of the event due to the impact of rising costs, Covid, Brexit and the war in Europe.
However, she dismissed suggestions the event was facing an “existential crisis” in the wake of the criticism in the open letter.
It was backed by many of the key players in a new eight-strong alliance of venues formed to allow them to promote shows and sell tickets together.
And Ms McCarthy, who has been at the helm of the Fringe Society for the past six years, described the recovery of the festival, which has more than 3,250 shows drawn from 58 countries confirmed so far for the 75th-anniversary edition, as “nothing short of a minor miracle”.
She expressed dismay the critics of the Fringe Society had gone into "nuclear mode" without speaking to her organisation over concerns the official festival app would not be returning this year amid warnings that it had “become increasingly difficult to justify the expense of taking part” in the festival.
The social media campaign, instigated by the Live Comedy Association and backed by more than 1,700 participants in the space of 24 hours, also raised concerns over a perceived lack of action and transparency over how emergency funding had been allocated, the rising cost of accommodation and the possibility of widespread rail disruption next month.
However, the open letter was backed by representatives of several venues, which had received emergency funding via the Fringe Society to help with their post-Covid recovery, including Assembly, Gilded Balloon, Just the Tonic, Laughing Horse, Pleasance and Underbelly.
Speaking at a media briefing to launch the 75th-anniversary programme, Ms McCarthy said she wanted to address the “noise” that had been generated by the open letter, which was circulated on Monday after it emerged over the weekend the official Fringe app would not be returning this year.
Ms McCarthy said: "I genuinely think it's nothing short of a minor miracle that the programme is here and we've got to this point. It should be a day of celebration.
“What we should be talking about is the shows, the context, the themes and the sheer 'wow' of this extraordinary festival after the drought of the last couple of years.
"I think everybody is hurting, basically. The last couple of years have really had its toll on people.
"People have forgotten that they asked us to delay the programme by a month to give artists and venues more time to register and be involved this year.
"There is a level of unease out there about where we are at the moment, because the programme would normally be out in June. I have huge empathy about that anxiety and worry.
“There seems to be something of a perfect storm conspiring against us. That's why I say it's a minor miracle that we have a programme this year.
"Covid, the war in Europe, Brexit, political instability, transport disruption, accommodation and inflation are all in the heads of artists and venues.
"We, as a team, are part of that and hugely empathise with people because it all worries us as much as it worries everybody else.”
Ms McCarthy issued a lengthy defence of the society in the run-up to the programme launch after the open letter demanded a response and “immediate, meaningful action” within 48 hours.
She pointed out the charity, which she said was almost “finished off” after the immediate impact of Covid left it facing insolvency, had lobbied the Scottish Government to provide emergency funding to the tune of £2.275 million of venues last year and this year.
Ms McCarthy admitted she was “surprised and disappointed” the Fringe Society had not been made aware of concerns directly before a critical open letter starting circulating online, but suggested “post-Covid anxiety” may have played a part in how the rift developed.
She said: “I think everybody is just a bit volatile at the minute and ready to just scream off because there is some level of a kind of post-traumatic stress syndrome, post-Covid, that people are dealing with.
“Normally you would expect people to talk to you first, to reach out and ask questions before going into that sort of nuclear mode.
“What I'm hearing from a lot of people is that they didn't know what our position was and had they known that first, they might not have signed the letter.
"The Fringe Society has not been exempt from the impacts of Covid. We're still working with a depleted team and a depleted budget.
“It’s absolutely impossible for us to deliver everything this year that we did in 2019. What we’re doing is the absolute best that we can in the most challenging of circumstances.”
Lyndsey Jackson, deputy chief executive of the Fringe Society, said: “I think the best thing we can do is continue to deliver a really good service that is ultimately focused on artists and audiences.
“Our job this year is to do the best job and offer the best service that we can, get artists and audiences together, and hopefully that will take the heat out of some of the tension.
“I think some of this is exposed because we have had two years of no Fringe. We’ve not really had any celebration or joy. I’m personally hopeful that the Fringe will be quite cathartic and healing in that sense.”