10:31 a.m. ET -- Tweet from @RafaelRomoCNN: "#Obama : #Iran dispute "has deep roots... it can't be overcome overnight." @CNNLive #UNGA
10:30 a.m. ET -- "I do believe that if we can resolve the issue of Iran's nuclear program, that can serve as a major step down a long road towards a different relationship -- one based on mutual interests and mutual respect," Obama said.
10:30 a.m. ET -- Obama outlines the U.S. policy toward the Middle East and North Africa: The United States is prepared to use "all elements of our power, including military force, to secure our core interests in the region" and confront threats to allies and partners. That includes taking action when it's necessary to defend America against terrorist attacks. Also, he said, the United States will ensure the free flow of energy to the world and confront threats to allies and partners. And the country will not tolerate the use and proliferation of weapons of mass destruction.
10:28 a.m. ET -- "In the near term," Obama said, "America's diplomatic efforts will focus on two particular issues: Iran's pursuit of nuclear weapons and the Arab-Israeli conflict. While these issues are not the cause of all the region's problems, they have been a major source of instability for far too long, and resolving them can help serve as a foundation for a broader peace."
10:25 a.m. ET -- "The notion that Syria can somehow return to a prewar status quo is a fantasy," Obama said. "It's time for Russia and Iran" to realize that insisting that Bashar al-Assad remains as Syria's president will actually ensure their greatest fears: It would increase the amount of space where violent extremists can operate, he said.
10:24 a.m. ET -- "I welcome the influence of all nations that can bring about a peaceful resolution of the Syrian civil war," Obama said.
10:23 a.m. ET -- The evidence is "overwhelming" that Syrian President Bashar al-Assad used chemical weapons against civilians, Obama said.
10:22 a.m. ET -- "An agreement on chemical weapons should energize a larger diplomatic" initiative, Obama said. He doesn't believe military action can achieve a lasting peace and said that Syrians themselves should decide who runs Syria.
10:20 a.m. ET -- Obama talked about the crisis in Syria and the "stillborn" peace process. The conflict "goes to the heart " of a bigger issue: "How should we respond to conflicts in the Middle East and North Africa?" That includes "conflicts between countries and conflicts within them."
10:19 a.m. ET -- Expanding on the theme of moving from a perpetual war footing, Obama says that "the world is more stable (than it was) five years ago." He became president nealy five years ago, you'll note. But dangers remain, he acknowledges, citing the current hostage crisis at a Kenya mall, a recent suicide bombing in Pakistan, and strife in the Middle East and North Africa.
10:15 a.m. ET -- Obama said that work has been done to end a decade of war, and he talked about "shifting away from a perpetual war footing."
10:12 a.m. ET -- President Obama underscored the importance of an institution like the United Nations. Once, he said, "the idea that nations and peoples could come together in peace to solve their disputes" seemed "unimaginable." But, he said, it took the "awful carnage" of two world wars to change thinking about that.
10:10 a.m. ET -- Obama has stepped up to the podium.
10:08 a.m. ET -- Rousseff has wrapped up her speech. U.S. President Barack Obama will be next.
10:06 a.m. ET -- Rousseff is calling for an expansion of the number of permanent members of the U.N. Security Council, no doubt with a view that Brazil should be among them. Criticizing the current setup -- what she called the "limited representation" on the council -- she said it has been unacceptably paralyzed in addressing such important issues as the Syrian conflict and the Israeli-Palestinian question.
10:02 a.m. ET -- Rousseff is hitting home the importance of the economy and mentions the need for reforms. "The world's economic situation remains fragile," she said. "We are all in the same boat."
10 a.m. ET -- Brazil will put forward proposals at the United Nations aimed at preventing the manipulation of cyberspace "as a weapon of war," and regulating states' behavior online, Rousseff said.
9:58 a.m. ET -- Rousseff talked about the issue of poverty -- a major concern of the world's nations. "Poverty is not a problem that is peculiar only to developing countries," she said.
9:54 a.m. ET -- Rousseff said Brazil would continue demanding explanations from the United States regarding its electronic surveillance programs exposed recently by former NSA contractor Edward Snowden, and it will seek guarantees that such acts will not continue. "Friendly governments that want strategic partnerships cannot possibly allow recurring and illegal actions to go on," she said.
9:53 a.m. ET -- The issue of privacy is not just relegated to a bilateral relationship, Rousseff said, referring to the United States and Brazil. The issue "affects" the entire world.
9:50 a.m. ET -- "Without a right to privacy," Rousseff said, "there is no real freedom of speech or freedom of opinion."
9:48 a.m. ET -- It didn't take long for Brazil's Rousseff to broach the subject of electronic spying. "Recently disclosed information on the activities carried out by a global network of electronic spying" has angered the world, she said.
9:48 a.m. ET -- Dilma Rousseff has started. She sent along her condolences to the families of victims in Nairobi, Kenya, where the terror group Al-Shabaab attacked a mall. She said "terrorism" should be condemned and there should be determination to tackle the problem.
9:45 a.m. ET -- Brazilian President Dilma Rousseff is moments away, it seems. Delegates are being reminded to speak at a calm pace so that translators can do their work easily.
9:33 a.m. ET -- Rousseff's state visit to Washington had been intended to bring the two biggest economies in the Americas closer together -- and the United States is Brazil's second-biggest trading partner after China. But reports alleging that the U.S. National Security Agency spied on Rousseff's mobile phone and e-mail communications embarrassed her, as CNN's Shasta Darlington reported last week.