9:28 a.m. ET -- Rousseff should be interesting from the U.S. government's point of view. Earlier this month, the U.S. and Brazil jointly agreed to postpone her planned October visit to Washington because of a controversy over reports that the U.S. government was spying on her communications.
9:27 a.m. ET -- A tweet from the United Nations: Ban Ki-moon to #UNGA : "Let us empower the United Nations to be more than a first responder or a last resort."
9:25 a.m. ET -- Ban has finished speaking. Soon will come Brazilian President Dilma Rousseff.
9:20 a.m. ET -- Ban has turned to Israel and the Palestinians. "If we are serious about achieving a two-state solution, then we must recognize that the window ... is closing fast."
9:19 a.m. ET -- In a related Syria item: We just learned, from Ban's associate spokesman Farhan Haq, that U.N. weapons inspectors will be back in Syria on Wednesday to assess at least a half a dozen claims of chemical weapons use in Syria -- some alleged to be regime use, others alleged to be rebel use. That note comes to us from CNN's Nick Thompson in London.
9:18 a.m. ET -- Ban said that the civil war in Syria has left the economy "in ruins" and communities "torn apart." "We face a moment of reckoning." He said Syria's government must obey international obligations regarding its chemical weapons stockpile but also stressed that the vast majority of the killing and atrocities have been carried out with "conventional weapons." He appealed to all states to end the arms flow into Syria.
9:15 a.m. ET -- Speaking about Syria, Ban said the international response to the chemical weapons problem in the devastated county has created "diplomatic momentum" for peace. "We must build on it to get the parties to the negotiating table," he said. "The only answer is a political settlement."
9:12 a.m. ET -- Ban has just called for a climate summit, to convene at the United Nations next September. He wants the summit to put nations on a path to a legal agreement on issues such as emissions, and to deliver an "inspiring new development framework."
9:10 a.m. ET -- Ban stressed the importance of the fostering the rights of women, who face abuse in many countries across the world. When girls are healthy and in school and "when women's lives are free of violence and discrimination, nations thrive." "Let the 21st century be the century of women."
9:04 a.m. ET -- Ban has kicked things off: "We come together not to preserve the status quo, but to drive our world forward." He's simultaneously giving a message of optimism and prodding -- he says our generation has the ability to "wipe poverty from the face of the Earth," but we're hindered by a number of problems, such as unresolved conflicts and youths without jobs.
8:59 a.m. ET -- We're just moments away from Ban's opening speech. After Ban will be Brazil's Rousseff, and then Obama.
8:56 a.m. ET -- Regarding Obama's speech this morning, scheduled for around 10:10 a.m.: He will focus on U.S. policy toward the Middle East and North Africa, a White House official said, according to CNN's Jim Acosta.
8:52 a.m. ET -- A tweet earlier this morning from Iranian Foreign Minister Mohammad-Javad Zarif: we have a historic opportunity to resolve the nuclear issue. 5+1 needs to adjust its posture commensurate with the new Iranian approach.
8:52 a.m. ET -- Secretary of State John Kerry, however, will be meeting with his Iranian counterpart, Foreign Minister Mohammad-Javad Zarif, at a Thursday meeting of the five permanent members of the U.N. Security Council, plus Germany. Discussions will surround restarting talks on Iran's nuclear program.
8:51 a.m. ET -- Could be a handshake. Could be more. Could be nothing. We'll see.
8:48 a.m. ET -- So how will Obama respond to Rouhani's overtures this week? No meeting between the two presidents has been scheduled, as far as we know. But a senior U.S. administration official said Tuesday that the White House has "left the door open" to some kind of face-to-face interaction between the two, CNN's Jim Acosta reported.
8:38 a.m. ET -- But Rouhani, a moderate politician elected in June, has called for better engagement with the West, including in a Washington Post op-ed last week, in which he called for nations to work together on contentious issues such as Iran's nuclear program. Iran says its nuclear program is for peaceful energy purposes; the United States and other Western nations accuse Iran of trying to develop a nuclear weapons program.
8:35 a.m. ET -- Another thing to look for today: What will Iranian President Hassan Rouhani say when he speaks this afternoon -- and will he interact with Obama? For the past several years, the General Assembly was then-Iranian President Mahmoud Ahmadinejad's chance to needle the United States and the West, with many Western diplomats often walking out on his speeches.
8:25 a.m. ET -- The United States is pushing for a U.N. Security Council resolution this week to enforce a deal, brokered by Russia and the United States, in which Syria would give up its chemical weapons -- a deal that came after a chemical weapons attack in the Damascus suburbs on August 21.
8:19 a.m. ET -- The General Assembly is a chance for about 200 countries to -- as our colleague Holly Yan puts it -- step up to the global stage and tell the world what they want. Among the hot topics you'll expect to be addressed: Syria, where more than 100,000 people have died since an uprising began there two years ago.
8:10 a.m. ET -- Tuesday's speeches will kick off around 9 a.m. with U.N. Secretary-General Ban Ki-moon. Brazilian President Dilma Rousseff will follow, with Obama scheduled to come right after her -- somewhere around 10:10 a.m.
7:56 a.m. ET -- It's a big day at the United Nations. Many world leaders are expected to speak at the General Assembly in New York over the next few days, with 34 -- including U.S. President Barack Obama -- speaking Tuesday.