While conceding that nations will disagree about when and how to step in as "tyrants ... commit wanton murder," President Obama told the U.N. General Assembly on Tuesday that "we must get better" at preventing atrocities.

The president again laid out his case for strong international action to hold Syrian President Bashar Assad accountable for his regime's alleged use of chemical weapons. Then Obama told world leaders that:

"While we need to be mindful that the world is full of unintended consequences, should we really accept the notion that the world is powerless in the face of a Rwanda or Srebrenica? If that's the world that people want to live in, then they should say so, and reckon with the cold logic of mass graves.

"I believe we can embrace a different future."

The president also used his address to say the U.S. is encouraged by signs that new Iranian President Hassan Rouhani is pursuing a "more moderate course." Obama also noted that "the supreme leader has issued a fatwa against the development of nuclear weapons, and President Rouhani has just recently reiterated that the Islamic Republic will never develop a nuclear weapon."

"Given President Rouhani's stated commitment to reach an agreement" about Iran's nuclear ambitions, Obama said, "I am directing [Secretary of State] John Kerry to pursue this effort with the Iranian government, in close coordination with the European Union, the United Kingdom, France, Germany, Russia and China. The roadblocks may prove to be too great, but I firmly believe the diplomatic path must be tested."

We live blogged as Obama spoke. Scroll down to read more.

As we reported earlier, the question of the day isn't about which topics the president will address, but whether he will or won't cross paths with Rouhani.

Update at 10:50 a.m. ET. World Cannot Be Powerless In The Face Of Mass Murder:

"We live in a world of imperfect choices," the president says. "Different nations will not agree on the need for action in every instance, and the principle of sovereignty is at the center of our international order. But sovereignty cannot be a shield for tyrants to commit wanton murder, or an excuse for the international community to turn a blind eye. While we need to be modest in our belief that we can remedy every evil. While we need to be mindful that the world is full of unintended consequences, should we really accept the notion that the world is powerless in the face of a Rwanda or Srebrenica? If that's the world that people want to live in, then they should say so, and reckon with the cold logic of mass graves.

"I believe we can embrace a different future.

"If we don't want to choose between inaction and war, we must get better – all of us – at the policies that prevent the breakdown of basic order. Through respect for the responsibilities of nations and the rights of individuals. Through meaningful sanctions for those who break the rules. Through dogged diplomacy that resolves the root causes of conflict, and not merely its aftermath. Through development assistance that brings hope to the marginalized. And yes, sometimes, all this will not be enough – and in such moments, the international community will need to acknowledge that the multilateral use of military force may be required to prevent the very worst from occurring."

Update at 10:45 a.m. ET. Greater Danger Is An America That Disengages:

Turning to a broader theme, Obama says that "the danger for the world is not an America that is eager to immerse itself in the affairs of other countries, or take on every problem in the region as its own. The danger for the world is that the United States, after a decade of war; rightly concerned about issues back home; and aware of the hostility that our engagement in the region has engendered throughout the Muslim World, may disengage, creating a vacuum of leadership that no other nation is ready to fill."

He continued: "I believe such disengagement would be a mistake. ...

"Some may disagree, but I believe that America is exceptional – in part because we have shown a willingness, through the sacrifice of blood and treasure, to stand up not only for our own narrow self-interest, but for the interests of all."

Update at 10:33 a.m. ET. On Iran, "Diplomatic Path Must Be Tested":

The U.S. is "encouraged that [Iranian] President Rouhani received from the Iranian people a mandate to pursue a more moderate course," Obama says.

"Given President Rouhani's stated commitment to reach an agreement, I am directing John Kerry to pursue this effort with the Iranian government, in close coordination with the European Union, the United Kingdom, France, Germany, Russia and China. The roadblocks may prove to be too great, but I firmly believe the diplomatic path must be tested. For while the status quo will only deepen Iran's isolation, Iran's genuine commitment to go down a different path will be good for the region and the world, and will help the Iranian people meet their extraordinary potential – in commerce and culture; in science and education."

Update at 10:30 a.m. ET. U.S. Is Prepared "To Use All Elements Of Our Power":

Staying on the Middle East, Obama says "the United States of America is prepared to use all elements of our power, including military force, to secure these core interests in the region. We will confront external aggression against our allies and partners, as we did in the Gulf War.

"We will ensure the free flow of energy from the region to the world. Although America is steadily reducing our own dependence on imported oil, the world still depends upon the region's energy supply, and a severe disruption could destabilize the entire global economy.

"We will dismantle terrorist networks that threaten our people. Wherever possible, we will build the capacity of our partners, respect the sovereignty of nations, and work to address the root causes of terror. But when its necessary to defend the United States against terrorist attacks, we will take direct action."

Update at 10:23 a.m. ET. Call For "Strong Security Council Resolution":

After saying the U.N. Security Council must endorse a strong resolution that ensures Syria will verify it is handing over its chemical weapons or face "consequences" if it fails to do so, Obama says that "if we cannot even agree on this," it will show that the U.N. is "incapable of enforcing even the most basic of international laws."

Update at 10:20 a.m. ET. "Insult" To Suggest Anyone Other Than Assad Used Chemical Weapons In August:

Speaking of the Aug. 21 chemical weapons attack near Damascus that the U.S. says killed more than 1,000 people, Obama says "it's an insult to human reason and to the legitimacy of this institution to suggest that anyone other than the regime carried out this attack."

Update at 10:15 a.m. ET. "Shifting Away From A Perpetual War Footing':

After withdrawing troops from Iraq and beginning a drawdown in Afghanistan, the U.S. is "shifting away from a perpetual war footing," Obama says.

He believes the "world is more stable than it was 5 years ago," but concedes that incidents such as the terrorist attack on a mall in Kenya show that dangers remain.

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