Prime Minister Benjamin Netanyahu added that he had also met with 20 heads of state who sought to strengthen their ties with Israel.
Saudi FM spoke at the United Nations General Assembly on Saturday.
Six or seven Muslim nations will join Saudi Arabia in making peace with Israel, they are expected to come from both Africa and Asia.
Netanyahu used the map to illustrate a new era of peace in the Middle East that would include the Palestinians, but critics say he sent the opposite message.
From warrior to statesman: Netanyahu's words resonated not just with the international audience but were a clarion call to his fellow Israelis to rally behind his vision.
Opposition head Yair Lapid attacked the PM, saying Netanyahu "ignored the fact that Israel is being torn apart due to his government."
Netanyahu: Tyrants in Tehran are nothing but a curse • "We must not give the Palestinians a veto over Israel's relations with Arab states"
When asked how they felt about the protests in the US in response to Netanyahu's visit, 53% of respondents stated they opposed protest action.
Israeli opponents of the judicial reform living in the US are making the most of the Israeli prime minister's visit to New York for the UNGA.
Palestinian Authority President Mahmoud Abbas used his platform at the UN General Assembly to bash Israeli actions and defend Palestinian terrorism as "peaceful resistance."
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