JERUSALEM — Prime Minister Benjamin Netanyahu of Israel introduced a new demand Friday for the final phase of negotiations over Iran’s nuclear program, saying the completed deal must include an “unambiguous Iranian recognition of Israel’s right to exist.”

Mr. Netanyahu, the world’s most vocal critic of the emerging agreement between six world powers and Iran, convened a special session of his security cabinet on Friday, hours before the onset of the Passover holiday, to review the framework agreement announced the night before.

He emerged saying the group “is united in strongly opposing the proposed deal,” contending it “would pose a grave danger to the region and to the world, and would threaten the very survival of the state of Israel.”

As the negotiations continued furiously in Lausanne, Switzerland, over the past week, Mr. Netanyahu made daily statements railing against them. He emphasized Iran’s involvement in regional conflicts, most recently Yemen, and denounced an Iranian general’s declaration in recent days that “the destruction of Israel is nonnegotiable.”