In his letter, Ayalon asked Richars Haas, the institute's president, to acknowledge his mistake and express remorse.
This is in fact a worse invitation because in the 1930s Hitler had not yet called for genocide, Ayalon wrote.
"But today we have learned the lesson – that appeasing fanatics like Hitler and granting them legitimacy leads to genocide and war," he said.
The Jewish leaders invited to the meeting with the Iranian president decided to boycott it. The event itself was embarrassing, with Ahmadinejad ignoring the questions directed at him and attacking the attendees for representing US President George W. Bush's stance.
I am deeply disappointed by the fact that the Council on Foreign Relations gave Iran's president the stage this week, Ayalon wrote.
"The very fact that an organization like the council convened to listen to his ranting provided Ahmadinejad legitimacy," he said.
The ambassador called the decision to host the Iranian leader a "Terrible mistake," Even though Ayalon said he was sure neither Haass nor any member of the council endorsed Ahmadinejad's views.
Legitimacy instead of condemnation
Not only America's relations with Israel should have dissuaded the council from inviting the Iranian president, according to Ayalon. He is also very hostile toward the US, as expressed in his UN appearances, the ambassador said.
Ahmadinejad said that the world would be better without America and also supports terror and works to harm American interests across the world, he added.
The ambassador wrote that letting Ahmadinejad speak would not change his approach but will only strengthen him.
Did you really expect to hear anything new from him, Ayalon asked Haas in the letter. The answer should be clear – what does a political leader have to say or do in order not to be worthy of your invitation, he added.
Richard Haas, the council's president and a Jew who has visited Israel many times in the past, was a senior State Department official working under former Secretary of State Colin Powell. The institute's board of directors includes Powell himself, former Secretary of State Madeleine Albright, and former US Ambassador to the UN Richard Holbrooke.
AP contributed to the report