Mr Huckabee said President Barack Obama was marching Israelis "to the door of the oven" - an apparent reference to the Nazi death camps.
The head of the Democratic National Committee said the statement had no place in US politics
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She said Mr Huckabee should apologise to the Jewish community.
Many US Republicans have strongly criticised the accord struck on 14 July which aims to curb Iran's nuclear programme in return for the easing of economic sanctions.
Israeli Prime Minister Benjamin Netanyahu has described the deal as a threat to Israel's survival
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The US Congress, which is dominated by the Republican party, has until 17 September to approve or reject the deal.
In an interview with a conservative website on Saturday, former Arkansas governor Mr Huckabee described the foreign policy of Mr Obama - a Democrat - as "the most feckless in American history".
"It is so naive that he would trust the Iranians. By doing so, he will take the Israelis and march them to the door of the oven," he told Breitbart News Saturday
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Mr Huckabee appeared to be referring to the Nazi death camps of World War Two in which millions of Jews and others were murdered.