Fergus Linehan said the festival was being made to work hard to shift tickets for shows due to a drop-off in the number of people booking up months in advance in the wake of the pandemic.
The Irishman, who has been at the helm of the festival since 2014, said the event had been hit by the trend which has been linked to concerns over whether live events will definitely be going ahead or ticketholders will end up missing them.
However Mr Linehan said Edinburgh and its festivals had a good track record at “riding out” difficult times previously.
And he welcomed the increased competition this August from events like the Edinburgh International Film Festival, which will be staged in full in August for the first time in 15 years, and the Connect musical festival, at Ingliston, which is being held over the last weekend in August.
The EIF, which announced its 75th anniversary at the end of March, is still selling tickets for some of its most high-profile productions, including Alan Cumming’s new Robert Burns-inspired dance-theatre Burn, physical theatre show Room, a new version of Liz Lochhead's acclaimed adaptation of the classical Greek tragedy Medea, starring Adura Onashile, and the Jungle Book reimagined as a dance show.
Mr Linehan said its classical musical concerts at the Queen’s Hall had been among the strongest sellers, even though they have traitionally attracted an older audience than other parts o the programme.
Mr Linehan said: “Bookings have been really solid for us so far, but we do need last-minute bookings as well.
“We know from trying to book them that hotel rooms in Edinburgh are really hard to find next month, but we don’t know how many of those people are going to wake up and want to go to a show.
“These things are so marginal for people putting on shows. If you walk into a theatre you can’t tell the difference between something that is 80 per cent or 90 per cent full, it just looks a big crowd, but a 10 per cent slide can be a big difference.
“We need a good strong August now, whereas in some previous years we would be pretty much home and hosed by now. They’re making us work hard for it.
“But it’s never the case that our shows are always booked up. Our venues are enormous. That’s just a myth.
“I know that some people are now not just into booking shows three or four months out. They have got suspicious that they will cancel or that they themselves will have to cancel. They are just not making those kind of long-range plans."
One of Mr Linehan’s first moves was to bring the EIF’s dates back into line with the Fringe to ensure they started and finished on the same day.
He admitted it would sound “crazy” if Edinburgh was to recommend to another city that it put all its major events at the same time.
But Mr Linehan said being part of large crowds in August was a key part of the appeal for festivalgoers and also cited the importance of the city’s festivals working closely together.
Mr added: "I have no regrets about moving the dates.
"It’s the interaction with the other art forms which is really exciting in Edinburgh.
"The crowd is the thing that people want and the love of the sense that you are where it is all going on.
“One of the advantages about the festivals working together in Edinburgh is that it stops the whole thing becoming too corporate.
"There is a feeling of all these cottage industries, as opposed to an enormous big event. If you go to a premier league football match you know what a corporate event is. It’s really not that.
"The fact that each festival has its own energy, can do its own thing and can work to its own business model creates freedoms that you just wouldn’t get if it was a hierarchical thing.
"I'm sure the festivals will continue to work together, but the independence of each of them is a real asset as well."
Mr Linehan pointed out that the combined strength of Edinburgh’s festivals withstood the impact of the global financial crisis in 2008 while other major events were “decimated.”
He said: “Festivals which have an incredibly strong identity and history sort of ride out these things. Edinburgh has got a very good track record in difficult times.
“When people have got choices to make I think they are still going to go to Edinburgh. It just has such a compelling offer.”
Mr Linehan revealed he would be moving to Australia with his family after this year's festival and was likely to miss the first event overseen by his predecessor, violinist Nicola Benedetti, the first Scot and the first woman to be appointed director.
However he added: “It think it’s incredible that Nicky has been appointed and I’m really excited by it.
"There are maybe three or four people in the world of classical music who can communicate to everyone, it’s a huge generational shift for the festival and she has amazing things to say about Scotlandt.
"There’s been real anxiety in the world of the arts about them becoming very managerial, and how it needs to move back from administrators and management structures to people whose lives are immersed in practice. That’s exactly what she is.
"She is grounded both in Scotland and in music. She is very young but has an entire performing career that most people wouldn’t have until they retire. She has built up this agency around the world. She is someone that we all listen to and respect. She has taken that and is doing something in Scotland with it.”