The former Arkansas governor made the tweet yesterday, a day after first making the comparison when denouncing President Barack Obama for his role in the agreement reached July 14 by the United States and five other world powers with Tehran.
Responding, Democratic National Committee Chairwoman Debbie Wasserman Schultz said Huckabee's statement was "grossly irresponsible" and called on him to apologise.
But a Huckabee spokeswoman said Sunday his comments reflect a longstanding position that "the Iran deal is a bad deal, bad for America and bad for Israel." Huckabee's tweet called on Congress to reject the nuclear deal.
"He's so naive he would trust the Iranians and he would take the Israelis and basically march them to the door of the oven."
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Obama, asked about the comments at a news conference in Addis Ababa, where he was meeting with Ethiopian officials, said they were part of a pattern of attacks by 2016 Republican presidential candidates that would be "considered ridiculous if it weren't so sad."
He said such issues as the Iran nuclear deal deserve serious debate, not outlandish statements.
In his initial remarks, Huckabee said that "this Iran deal should be rejected by both Democrats and Republicans."
"We forget Iranians have never kept a deal in 36 years under the ayatollah. There's no reason to think they will suddenly start doing it."
Huckabee said about the deal: "I read the entire thing. We gave away the whole farm. It's got to be stopped."
Huckabee's comments come as the Republican presidential candidates struggle to break through with 16 presidential candidates already in the Republican field, and one of those, New York businessman Donald Trump, getting more attention than most.