United Nations (CNN) -- Here are three things we learned Thursday at the United Nations General Assembly in New York.
1. Palestinians begin consultations with member states about seeking non-member-state status
"We are confident that the vast majority of the countries of the world support our endeavor aimed at salvaging the chances for a just peace," Palestinian Authority President Mahmoud Abbas said. "In our endeavor, we do not seek to delegitimize an existing state -- that is Israel -- but rather to assert the state that must be realized -- that is Palestine."
Then, departing from his prepared speech, Abbas added, to applause: "We are not attempting to delegitimize them, they are trying to delegitimize us."
Abbas said Palestinians were facing "a campaign of ethnic cleansing" in which they are being denied full access to houses of worship, schools, hospitals and housing.
"The occupying power is also continuing its construction and expansion of settlements in different areas throughout the West Bank," he told the assembly.
Israel rejects a Palestinian state and refuses to end its occupation, Abbas said.
"I speak on behalf of an angry people," he said. "Israel continues to enjoy impunity."
Last year, the Palestinian Authority failed in its bid to win U.N. recognition as an independent state.
Israeli President Benjamin Netanyahu rejected Abbas' remarks. "I say to him and I say to you, we won't solve our conflict with libelous speeches at the U.N.," he told the assembled heads of state. "We won't solve our differences with a unilateral declaration of statehood. We have to sit together, negotiate together and reach a mutual compromise in which a demilitarized Palestinian state recognizes the one and only Jewish state."
He said Israelis "seek to forge a durable peace" with the Palestinians.
2. Israel calls for a 'red line' on Iran
For Israel, the issue of how to respond to Iran's nuclear program has strained relations between Netanyahu and U.S. President Barack Obama. Tehran insists its nuclear program is for peaceful purposes, but Western leaders say they believe it is aimed at building a weapon.
"Shockingly, some people have begun to peddle the absurd notion that a nuclear-armed Iran would actually stabilize the Middle East, Netanyahu said. "Yeah, right. That's like saying a nuclear-armed al Qaeda would usher in an era of universal peace."
Netanyahu called for "a clear red line" on what he described as "Iran's nuclear weapons program."
Such lines prevent wars, he said, citing the Cuban Missile Crisis as an example where former President Fidel Castro backed down in the face of a U.S. threat.
In the case of Tehran, "the red line must be drawn on Iran's nuclear enrichment program," he said. "Because these enrichment facilities are the only nuclear installations that we can definitely see and credibly target. And I believe that, faced with a clear red line, Iran will back down. And this will give more time for sanctions and diplomacy to convince Iran to dismantle its nuclear weapons program all together."
Israel seeks international urgency, as negotiations aimed at curbing Iran's nuclear ambitions have failed to produce an agreement.
Obama has laid out his own red-line of sorts, saying a decision by Iran to go nuclear and a move to assemble a bomb would prompt him to act.
Defense Secretary Leon Panetta said last month the United States had no intelligence to indicate a decision by Iran to go after the bomb.
But Netanyahu, Israeli Defense Minister Ehud Barak and others argue Iran can continue to develop the expertise and technology needed to make a bomb and gain this breakout capacity without having made an official "decision."
Iranian leader Mahmoud Ahmadinejad said his country won't be influenced by a threat from Israel and a demand from Obama to abandon plans to acquire nuclear weapons.
"It does not impact our policies in the slightest," Ahmadinejad told CNN's Fareed Zakaria in an interview to be aired Sunday at 10 a.m. and 1 p.m. Eastern.
"Iran is a vast country. It's a great country. Let's assume a few terrorists come and assassinate some of our officials. Will the country be damaged? No. A couple of bombs will be set to explode. Will the country be destroyed? No.
"We see the Zionist regime at the same level of the bombers and criminals and the terrorists. And even if they do something -- even if they do something, hypothetically, it will not affect us fundamentally," Ahmadinejad said.
Also reacting to Netanyahu was Hanan Ashrawi, a member of the executive committee of the PLO.
"This whole theory of red lines is a theory that is not only counterproductive, but will backfire," she told CNN in Ramallah. "Once you issue an ultimatum you have to follow through and it is obvious that in a volatile situation, beginning to issue not just ultimatums, but red lines and deadlines, you are courting disaster."
3. U.N.'s top diplomat gets a prank call
As he was involved in a series of meetings with presidents and prime ministers, Secretary-General Ban Ki-moon was told Wednesday that Canadian Prime Minister Stephen Harper was on the phone.
Ban took the call and listened as the caller discussed fetuses and the abortion issue. Ban heard the French speaker apologize for not attending the meeting and having instead sent his foreign minister, whom he referred to as his "pet dog."
When the caller said he needed help combing his hair with Crazy Glue, Ban asked whether the caller was really the prime minister.
The caller eventually handed the phone to a collaborator, who appealed to Ban to press NHL Commissioner Gary Bettman to return the Avalanche hockey team to Quebec from Colorado. At that, the call ended; it's not clear who hung up first.
A U.N. spokesman, who confirmed the prank call, said Ban took it in the spirit in which it was intended.
The callers are believed to be part of the "Masked Avengers," a group that specializes in such hijinks, once fooling Sarah Palin.
CNN's Sara Sidner, Richard Roth, Joe Vaccarello and Elise Labott contributed to this report