More than 120 presidents, prime ministers and monarchs will attend the 67th session of the United Nations General Assembly this week in New York.
The annual meeting comes as war rages in Syria, deadly protests spread across the Middle East and tensions ramp up between Iran and Israel.
Monday, Iranian President Mahmoud Ahmadinejad addressed the assembly with heated rhetoric despite a warning by U.N. Secretary-General Ban Ki-moon against incendiary speech.
"Fundamentally, we do not take seriously threats of the Zionists," Ahmadinejad said. "We believe the Zionists see themselves at a dead end and they want to find an adventure to get out of this dead end. While we are fully ready to defend ourselves, we do not take these threats seriously."
He also sought to delegitimize Israel's historic ties to the Middle East and the country's political and military power in the region and the world, saying that Israelis "do not even enter the equation for Iran."
Monday's comments prompted a walkout by the Israeli delegation.
In addition to not recognizing Israel's sovereignty, Ahmadinejad denied that Tehran is providing weapons or training to the Syrian government of President Bashar Assad.
He also restated that his country's uranium enrichment project is only for peaceful purposes and a matter of dialogue between his country and the United States, stressing the importance of fairness, dialogue and respect for others.
It was the Iranian president's eighth visit to the U.N. gathering held each September. He said this would be his last trip to New York as president of Iran, because his term is ending and he is barred from seeking a third consecutive term.
President Barack Obama was also in New York, Monday. However his first stop was for an appearance with first lady Michelle Obama for a taping of ABC's "The View."
Critics have accused Mr. Obama of being more concerned about his re-election effort than talking directly to other world leaders.
The president is scheduled to deliver a major speech to the assembly Tuesday addressing anti-American protests in the Arab world but has left the one-on-one meetings to Secretary of State Hillary Clinton.