When asked whether he didn't think it was problematic to support a party whose leader described Berlin's Holocaust memorial as a "monument of shame," Eitan said: "I haven't heard about that."
Eitan also said he was not bothered by fact senior AfD member Beatrix von Storch, whom he mentioned by name in his message of support, is the granddaughter of Lutz Graf Schwerin von Krosigk, who served as finance minister under Adolf Hitler.
"We're three generations after the Holocaust, and the opinions and the entire world are changing right before our eyes," he explained. "The media, the internet, this entire system is causing a fundamental social change all over the world. This is why we need to treat people, communities, countries and parties in a global manner. There's no escaping that."
He expressed confidence that AfD would "help Israel with anything we'll ask of them."
The anti-immigration party posted Eitan's message of support on its website, and quoted him as saying that "The Muslim world and its culture are very different than the Western one. Any place where there are Muslims today, in any European country, violence and terrorism can be expected as a result."
Eitan explained that he did not use these exact words, saying "The new Muslim generation, the young people, they are greatly influenced by 'Islamic Imperialism,' the Islamic issue with the fact we're not all Muslims, that we are heathens. As a result, there's a risk in all European nations, where there are large concentrations of Muslims, for terrorism and attacks, especially against Jews."
"I've offered this party several times in the past to set up a system that would take care of refugees in Muslim countries, that would take the Muslims to the culture of their countries, and thus prevent the violent acts we witness in Europe," he added.
The 91-year-old Eitan, who led the Mossad operation to capture Nazi criminal Adolf Eichmann, recorded the message of support ahead of an event against anti-Semitism the party was organizing at the German parliament.
"I wholeheartedly wish that you would be strong enough to stop the open borders policy, to stop the Islamization of your country, and to protect your citizens from terrorism and crime," the former minister, who was portrayed by AfD as the "legend of Israeli secret services," was quoted as saying.
"As a friend of Germany, I advise you: Close the borders to mass Muslim immigration as soon as possible. Make international alliances that would help offer a solution to the asylum seekers outside of your country. Muslim refugees need to find refuge in Muslim countries."
Israel's Ambassador to Germany Jeremy Issacharoff slammed Eitan's message, saying "It's hard to believe that the man who captured Eichmann and brought him to Israel to face justice is capable of praising German far-right elements that so admire their Nazi past, and to even go as far as to wish this would be an alternative for Europe! Sad and disgraceful."
Itay Mashiach contributed to this report.