"No nation should possess nuclear weapons," Rohani, whose country is accused by western countries of seeking an atomic bomb, told a UN General Assembly meeting on nuclear disarmament.
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"As long as nuclear weapons exist, the risk of their use, threat of use and proliferation persist. The only absolute guarantee is their total elimination," Rohani said.
He called on Israel to join the Non-Proliferation Treaty, which aims to put nuclear weapons under international controls and prevent their spread.
Israel, which is widely believed to have nuclear weapons but has never acknowledged its program, has not signed the treaty, unlike Iran.
"Almost four decades of international efforts to establish a nuclear-weapon-free zone in the Middle East have regrettably failed," Rohani said.
"Israel, the only non-party to the Non-Proliferation Treaty in this region, should join thereto without any further delay," Rohani said.
The Iranian leader, who generally does not refer to Israel by name, was speaking in his role as head of the Non-Aligned Movement.
Rouhani, a self-described moderate in the clerical regime who swept to power in June, has urged a quick resolution of a standoff with Western powers over Iran's contested nuclear program.
Israeli Prime Minister Benjamin Netanyahu has spearheaded criticism of Rouhani, calling him a "wolf in sheep's clothing" and urging no let-up in pressure on Iran.
Netanyahu has charged that Iran, which says its nuclear work is for peaceful purposes, is seeking a nuclear weapon and has not ruled out an Israeli military strike.
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