JERUSALEM — Prime Minister Benjamin Netanyahu and Defense Minister Ehud Barak have turned into the odd couple of Israeli politics in whose hands sits the prospect of an attack on Iran. From opposite political traditions with distinct experiences and worldviews, the two have forged a tight bond, often excluding the rest of the Israeli leadership.

For Mr. Netanyahu, an Iranian nuclear weapon would be the 21st-century equivalent of the Nazi war machine and the Spanish Inquisition — the latest attempt to destroy the Jews. Preventing that is the mission of his life. For Mr. Barak, who spurns talk of a second Holocaust and fear for Israel’s existence, it is a challenge about strategy: “zones of immunity” and “red lines,” the operational details of an assault on Iran’s nuclear facilities.

“All leaders have kitchen cabinets, but Netanyahu and Barak have established a kitchenette of two,” remarked Nahum Barnea, a columnist for the Yediot Aharonot newspaper, in an interview. “They haven’t discussed Iran with the rest of the government in weeks and have convinced themselves there is only one way to deal with Iran — their way.”

A top Israeli official who works closely with both leaders and spoke on the condition of anonymity confirmed that the cabinet had not talked lately about Iran, but noted that detailed and long-standing preparation had gone into the possibility of a military strike. Of the two men, he said: “One views himself as a savior, the other lives for a good operation. They’re a strange pair who have come to appreciate each other. Together they control this issue.”