The fallout over Republican presidential candidate Mike Huckabee's controversial remarks on the Iran nuclear deal has now reached Israel.

Over the weekend, Huckabee derided the deal announced in Vienna between six world powers and Iran, saying it would "take the Israelis and march them to the door of the oven." The comments, which invoked the Holocaust in criticizing the agreement — it restricts Tehran's nuclear program in exchange for sanctions relief — earned swift condemnation from the Anti-Defamation League, comedian Jon Stewart and congressional Democrats, as well as President Obama.

Huckabee, as my colleague Jose A. DelReal noted, made hay with the controversy, responding to Obama's censure with a new attack on the president's supposed blindness to the real threat that Iran poses.

Criticism now, though, has come from a constituency the former Arkansas governor would probably be less inclined to offend: Israel.

Yisrael Katz, the country's transport minister and a close ally of Prime Minister Benjamin Netanyahu, said on Facebook that although he appreciated Huckabee's concern for Israel, the comments went a bit too far.

"Respected Mr. Huckabee: nobody marches the Jews to ovens anymore," Katz said. "To this end we established the State of Israel and the [Israel Defense Forces]; and, if need be, we will know how to defend ourselves, by ourselves."

Katz was not alone in raising an objection.

"These are not words that I would use or that I think are appropriate," said Ron Dermer, Israel's ambassador to the United States, stressing that despite his opposition to the deal, he didn't believe the White House was acting in bad faith.

"Look, we have a very serious disagreement with the administration on a very serious issue," Dermer told USA Today. "But what I don't doubt is the sincerity of the president or his team when they say they believe this deal not only makes America safe but makes Israel safe. Where we disagree is the judgment of actually what this deal is going to do."

A former U.S. envoy to Israel had a harsher reaction to Huckabee's rhetoric.

"There are serious issues to be debated here, but for anybody to equate what the president’s doing to what Adolf Hitler did in World War II is just extraordinary," Daniel Kurtzer, who served under the George W. Bush administration, told MSNBC.

"And in some ways it’s a form of incitement, and we’ve seen the results of that 20 years ago in Israel," he added, referring to the toxic political climate that led to the assassination of Israeli Prime Minister Yitzhak Rabin by a right-wing Israeli radical in 1995.

"I just hope that people really stand back and understand that Mr. Huckabee has crossed a very serious line here. Every Republican candidate should stand up, condemn this and ask him to retract it," Kurtzer said.

Huckabee, for his part, appears to have doubled down on the comments.

"The response from Jewish people has been overwhelmingly positive. The response from Holocaust survivors, from the children of Holocaust survivors.... People were overwhelmingly supportive," Huckabee said Tuesday on NBC's "Today" show.

On Monday, he returned to the metaphor of World War II.

"If we don’t take seriously the threats of Iran, then God help us all. Because the last time — it’s Neville Chamberlain all over again. We’re gonna just trust that everyone’s gonna do the right thing," he told Fox News. "Three times I’ve been to Auschwitz. When I talked about the oven door, I have stood at that oven door. I know exactly what it looks like.”

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