Editor's note: President Barack Obama addressed the U.N. General Assembly on Tuesday. You can read a live blog of his remarks below or see his remarks in full here.

[Updated at 10:51 a.m. ET] President Obama pointed to all of the Libyans who supported America and showed their love of Ambassador Chris Stevens as further hope for the world. He's bringing the speech full circle by going back to the attacks in Benghazi.

"Today I promise you this – long after these killers are brought to justice, Chris Stevens’ legacy will live on in the lives he touched. In the tens of thousands who marched against violence through the streets of Benghazi; in the Libyans who changed their Facebook photo to one of Chris; in the sign that read, simply, Chris Stevens was a friend to all Libyans,'" Obama said. "They should give us hope. They should remind us that so long as we work for it justice will be done; that history is on our side; and that a rising tide of liberty will never be reversed.""

[Updated at 10:50 a.m. ET] President Obama is talking about the hope he sees in the communities around the world like Jakarta, Seoul, Prague and others.

"These men, women and children of every race and every faith remind me that for every angry mob that gets shown on television, there are billions around the globe who share similar hopes and dreams. They tell us that there is a common heartbeat to humanity," he said. "So much attention in our world turns to what divides us. That’s what we see on the news, and that consumes our political debates. But when you strip that all away, people everywhere long for the freedom to determine their destiny; the dignity that comes with work; the comfort that comes from faith; and the justice that exists when governments serve their people – and not the other way around."

[Updated at 10:48 a.m. ET] President Obama says that while he has seen a lot of troubling things in recent times, he believes he has witnessed a similar amount of progress that leaves him hopeful.

"The war in Iraq is over, and our troops have come home. We have begun a transition in Afghanistan, and America and our allies will end our war on schedule in 2014," Obama said. "Al Qaeda has been weakened and Osama bin Laden is no more. Nations have come together to lock down nuclear materials, and America and Russia are reducing our arsenals. I’ve seen hard choices made – from Naypyidaw to Cairo to Abidjan – to put more power in the hands of citizens."

[Updated at 10:46 a.m. ET] President Obama is now addressing the concerns about a  nuclear Iran and the policies and ideology of leader Mahmoud Ahmadinejad.

"In Iran, we see where the path of a violent and unaccountable ideology leads. The Iranian people have a remarkable and ancient history, and many Iranians wish to enjoy peace and prosperity alongside their neighbors. But just as it restricts the rights of its own people, the Iranian government props up a dictator in Damascus and supports terrorist groups abroad," Obama said. "Time and again, it has failed to take the opportunity to demonstrate that its nuclear program is peaceful, and to meet its obligations to the United Nations."

Obama said that he would like to solve these issues with diplomacy - and it is still possible.

"But that time is not unlimited. We respect the right of nations to access peaceful nuclear power, but one of the purposes of the United Nations is to see that we harness that power for peace," Obama said. "Make no mistake: a nuclear-armed Iran is not a challenge that can be contained."

[Updated at 10:45 a.m. ET] Obama is now talking about the conflict in Syria.

"The future must not belong to a dictator who massacres his people. If there is a cause that cries out for protest in the world today, it is a regime that tortures children and shoots rockets at apartment buildings," Obama said. "And we must remain engaged to assure that what began with citizens demanding their rights does not end in a cycle of sectarian violence. "

Deaths mounting in Syrian towns; children being tortured, U.N. official says 

[Updated at 10:44 a.m. ET] Obama is now addressing the peace process in Israel.

"Among Israelis and Palestinians, the future must not belong to those who turn their backs on the prospect of peace. Let us leave behind those who thrive on conflict, and those who reject the right of Israel to exist," he said. "The road is hard but the destination is clear – a secure, Jewish state of Israel; and an independent, prosperous Palestine. Understanding that such a peace must come through a just agreement between the parties, America will walk alongside all who are prepared to make that journey."

[Updated at 10:42 a.m. ET] President Obama is referencing a quote by Gandhi: "Intolerance is itself a form of violence and an obstacle to the growth of a true democratic spirit."

Obama says that we must all not just condemn the recent video and slander of Islam.

"Yet to be credible, those who condemn that slander must also condemn the hate we see when the image of Jesus Christ is desecrated, churches are destroyed, or the Holocaust is denied. Let us condemn incitement against Sufi Muslims, and Shiite pilgrims," he said.

[Updated at 10:40 a.m. ET] President Obama warned that while violence may initially be voiced against the West it will eventually spread if nothing is done.

"The same impulses toward extremism are used to justify war between Sunnis and Shia, between tribes and clans. It leads not to strength and prosperity but to chaos," Obama said. "In less than two years, we have seen largely peaceful protests bring more change to Muslim-majority countries than a decade of violence. Extremists understand this. And because they have nothing to offer to improve the lives of people, violence is their only way to stay relevant. They do not build, they only destroy."

He called on leaders and those who have protested during the Arab spring to reclaim the future.

"The future must not belong to those who target Coptic Christians in Egypt – it must be claimed by those in Tahrir Square who chanted 'Muslims, Christians, we are one.'  The future must not belong to those who bully women – it must be shaped by girls who go to school, and those who stand for a world where our daughters can live their dreams just like our sons," Obama said. "The future must not belong to those corrupt few who steal a country’s resources – it must be won by the students and entrepreneurs; workers and business owners who seek a broader prosperity for all people. Those are the men and women that America stands with; theirs is the vision we will support."

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