Nick Barley said there was still availabilty for events he would have expected to sell out almost immediately previously.
He cited the changes in buying patterns which have been seen across the festivals and events sector in the wake of the pandemic as the key factor.
Mr Barley said the festival, which would previously expect to sell 80 per cent of its tickets on the day its box office opened, had seen a spike since the start of the other festivals in the city last week.
Mr Barley, who has programmed more than 600 events across 18 days from this Saturday, said it was a “miracle” that the city’s festivals have been able to return on the scale they have this year.
However he insisted it may take several years for the week festival to recover from the impact of Covid restrictions, which forced the festival to go completely online in 2020.
The book festival returned last year in a “hybrid” form before socially-distanced audiences at a new home at Edinburgh College of Art.
There will be nine separate spaces for events there this year, while the festival will also use the 750-capacity Central Hall for its biggest events.
In-person events featuring First Minister Nicola Sturgeon, comic Frankie Boyle, singer-songwriters Martha Wainwright and Ricky Ross, and the former Scots Makar Liz Lochhead are among those which are still on sale on the festival website.
Tickets are also still available for appearances by the authors Ali Smith, Val McDermid, Michael Morpurgo, Denise Mina, Louise Welsh and Naom Chomsky.
Mr Barley said: “In 2017, 2018 and 2019, our ticket buying patterns were phenomenal and the envy of the world.
“We were selling 80 per cent of all our tickets withing four hours of them going on sale. We had a much slower start. We hit our target, but it was a much lower target.
"We still have to sell a lot more tickets and rely more on walk-ups than we’ve ever had to do before. We've got a huge amount of work to do.
“We’ve still got tickets on sale for events that would have sold out within a couple of hours before.
"We need to get that message out that there is a fantastic opportunity for people who have missed out on the book festival in the past to see some of the greats, not only of literature, but also of music and film.
"Like all the other festivals, we don’t quite know what it’s going to feel like. I’m just crossing my fingers that we can deliver in the same way that the Fringe, the International Festival and the Tattoo are doing.
“I think it’s a miracle that what we recognise as Edinburgh’s festivals have come back this year.
"We’ve had to dig deep to keep our own festival alive. The fact that we can have a festival of scale this year is a real tribute to my team. I still think it is going to be another two or three years, at least, before we’re really sure that we’ve survived.”