The presidential candidate Mike Huckabee has said the deal between six world powers and Iran regarding the Islamic Republic’s nuclear ambitions will “take the Israelis and march them to the door of the oven”.

The former Arkansas governor made the comment, with its allusion to the Holocaust, in a conversation with the conservative news site Breitbart.com.

“This president’s foreign policy is the most feckless in American history,” he said. “It is so naive that [Barack Obama] would trust the Iranians. By doing so, he will take the Israelis and march them to the door of the oven.

“This is the most idiotic thing, this Iran deal. It should be rejected by both Democrats and Republicans in Congress and by the American people. I read the whole deal. We gave away the whole store. It’s got to be stopped.”

In response, Debbie Wasserman Schultz, the chair of the Democratic National Committee, said: “Cavalier analogies to the Holocaust are unacceptable. Mike Huckabee must apologize to the Jewish community and to the American people for this grossly irresponsible statement.”

The National Jewish Democratic Council (NJDC) said it “denounced” Huckabee’s comments “in the strongest possible terms” and called on the other 15 Republican presidential candidates to follow suit.

An NJDC statement said: “Far, far too often, this organization has found itself forced to denounce politicians for invoking the Holocaust in inappropriate and offensive ways. These comments by Governor Mike Huckabee, however, may be the most inexcusable we’ve encountered in recent memory.

“To state that President Obama is leading Israelis ‘to the door of the oven’ is not only disgustingly offensive to the president and the White House, but shows utter, callous disregard for the millions of lives lost in the Shoah and to the pain still felt by their descendants today.”

Huckabee, meanwhile, doubled down.

Tell Congress to do their constitutional duty & reject the Obama-Kerry #IranDeal --> http://t.co/SaIyuq4w01 pic.twitter.com/2rFJgdDHhV — Gov. Mike Huckabee (@GovMikeHuckabee) July 26, 2015

The deal between Iran and the US, Russia, Germany, France, Britain and China was reached in Vienna two weeks ago. Iran accepted restrictions on its nuclear ambitions – including the elimination of 98% of its uranium stockpile and the removal of two-thirds of its uranium-enriching centrifuges – in return for the lifting of economic sanctions.

Opposition from Israel has been fierce, with fire turned on prime minister Binyamin Netanyahu. Immediately after the accord was announced, the leader of the Jewish state called it a mistake of historic proportions.

“Iran is going to receive a sure path to nuclear weapons,” he said. “Iran will get a jackpot, a cash bonanza of hundreds of billions of dollars, which will enable it to continue to pursue its aggression and terror in the region and in the world. This is a bad mistake of historic proportions.”

Defense secretary Ash Carter visited Israel and other allies this week. In Israeli circles, attention turned to stoking support in the US Congress.

Among Republicans and hawkish Democrats, reaction has been hostile. This week, Secretary of State John Kerry, Treasury secretary Jack Lew and Energy secretary Ernest Moniz appeared before the GOP-controlled Senate foreign affairs committee to defend the deal.

Public opinion in the US is split on the deal, but with President Obama wielding a veto, Congress is unlikely to be able to successfully defeat it. Republican 2016 candidates including the Florida senator Marco Rubio have said that if elected, they would undo it from the White House.

John Kerry defends the Iran deal in front of the Senate foreign relations committee. Guardian

Huckabee, a rightwing populist with a strong appeal in evangelical circles, finished second in the Republican primaries in 2008 after winning the Iowa caucus. He went on to work as a host for Fox News.

Running for the White House a second time, he is lagging in the 16-strong GOP field, which was led in a CNN poll released on Sunday by Donald Trump, Jeb Bush and Scott Walker. Only the top 10 GOP candidates will participate in the first debate, in Cleveland on 6 August.

In its statement, the NJDC added that though “it is almost pointless to demand Governor Huckabee apologize for his remarks”, other Republican candidates should do just that.

“Republicans have fallen over themselves to speak out against Donald Trump’s outrageous rhetoric on immigration and veterans,” the NJDC said. “Will they now do the same and speak out against this unacceptable attack against President Obama that smears the memory of Holocaust victims … or will they stand by in silence and implicit approval?”

Talking to Breitbart about his high favourability ratings, Huckabee said: “People don’t vote for someone they don’t like. So I just got a make sure I don’t start doing stuff that make people stop liking me.”