Sir Jonathan Mills said it was understandable people would protest against the actions of the Israeli government during the month-long war which, according to the United Nations, has killed nearly 1,900 Palestinians and 67 Israelis, many of them civilians.
However, he said it was "regrettable" that Incubator Theatre of Israel, which has funding from its government, had cancelled Fringe show The City after public protests and opposition from leading Scottish cultural figures.
Speaking ahead of tomorrow's opening of his last festival as director, Sir Jonathan pointed to similar action in 2012 against a show by the Batsheva Dance Company of Israel. In that case, the performances continued.
He said: "I think it is regrettable, but several years ago we had a similar situation and we worked very closely with the company to make sure it did not cancel it.
"Protest by all means, peacefully where possible. It is one thing to protest against the government of Israel - who wouldn't in the current circumstances? It is entirely different to protest against an artistic group, because my concern is, if we close down that space, what is left? There is no dialogue and that is no good for anyone."
In an interview on Monday, before Incubator Theatre announced the permanent cancellation of the show last night, Sir Jonathan said: "If Israel is isolated, then I believe the plight of individuals in Gaza are all the more precarious. We have seen that time and time again, where regimes are isolated, it does not have the effect we intend and so I feel very strongly it is a very unfortunate circumstance."
He said very few arts organisations were not funded in some way by a government.
"The Royal Shakespeare Company is funded by the British Government - does that mean we should not have it because we object to the war in Iraq?" he asked.
"Where does that process stop? And do we accept there is a distinction between an organisation being funded by a government and an organisation speaking for that government? I don't believe that is the case here."
Underbelly said yesterday: "We are very disappointed to announce we have been unable to find a space viable for the show and for the security of the audience."
Sir Jonathan also said the Commonwealth Games had been a great success. "I think there was a deep appreciation of these Games," said the Australian.
"I don't want to sound blase, but we do that kind of festival every year in Edinburgh - it is longer and there are more artists than athletes in the Games.
"But the more places in Scotland experience these events, we hope they appreciate what is here on an annual basis."
The festival opens with a concert by the Royal Scottish National Orchestra at the Usher Hall.