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Instead, he told aides it was the kind of self-defeating behaviour he had come to expect from Mr Netanyahu, according to Goldberg, who is renowned for having close ties to both leaders.

The president believes each new settlement announcement is driving Israel towards a “near total” international isolation that presents a greater long-term threat to its survival than Iran’s nuclear programme, which American and Israeli officials believe is aimed at producing a bomb.

“If Israel, a small state in an inhospitable region, becomes more of a pariah – one that alienates even the affections of the US, its last steadfast friend – it won’t survive,” Goldberg writes, paraphrasing Mr Obama’s words. “Iran poses a short-term threat to Israel’s survival; Israel’s own behaviour poses a long-term one.” Mr Obama also believes the Israeli prime minister is a “political coward” who is incapable of making concessions to the Palestinians because he has “become captive of Jewish settler lobby”.

Iran poses a short-term threat to Israel’s survival; Israel’s own behaviour poses a long-term one

His faith in Mr Netanyahu has sunk so low that he is unwilling to spend more time on pursuing fresh peace initiatives, despite the enthusiasm of the presumptive new US secretary of state, John Kerry, for new talks.

“What Obama wants is recognition by Netanyahu that Israel’s settlement policies are foreclosing on the possibility of a two-state solution, and he wants Netanyahu to acknowledge that a two-state solution represents the best chance of preserving the country as a Jewish-majority democracy,” Goldberg wrote.

The report coincided with briefings from Israeli officials that Mr Netanyahu will meet Mr Obama in Washington in early March if he retains power after next week’s Israeli general election. It would be the first meeting of the two men for a year. Mr Netanyahu will also address the American Israel Public Affairs Committee (AIPAC), America’s most influential pro-Israeli lobby group, during the visit.

A spokesman for Mr Netanyahu’s office declined to comment on the latest report.