The Note's Must-Reads are a round-up of today's political headlines and stories from ABC News and the top U.S. newspapers. Posted Monday through Friday right here at www.abcnews.com

Compiled by ABC News' Jayce Henderson, Amanda VanAllen, Will Cantine and Jordan Mazza

PRESIDENT OBAMA, IRAN AND THE U.N. ABC News' Dana Hughes: " Iran: We're No Threat, Warns Against Syria Strikes" In his first public address on the global stage at the United Nations, new Iranian President Hassan Rouhani had a message for President Obama: Iran poses no security threat to the world or the region. "In fact, in ideals as well as in actual practice, my country has been a harbinger of just peace and comprehensive security," Rouhani said. LINK

The Wall Street Journal's Jay Solomon and Carol E. Lee: " Iran Applies Brakes to U.S. Mideast Plans" President Barack Obama argued the U.S. case before world leaders for resolving the Middle East's deepest conflicts, but pushback from Iran dimmed hopes that had been building for a rapid leap forward. Iranian President Hasan Rouhani's decision against meeting Mr. Obama-or even exchanging a handshake-at the U.N. General Assembly in New York on Tuesday soured what American and European officials had hoped would mark an advancement in efforts to wind down tensions. LINK

The New York Times' Mark Landler: " Obama Defends U.S. Engagement In The Middle East" President Obama on Tuesday laid down a retooled blueprint for America's role in the strife-torn Middle East, declaring that the United States would use all of its levers of power, including military force, to defend its interests, even as it accepted limits on its ability to influence events in Syria, Iran and other countries. In a wide-ranging speech to the General Assembly that played off rapid-fire diplomatic developments but also sought to define what he called a "hard-earned humility" about American engagement after 12 years of war, Mr. Obama insisted that the United States still played an "exceptional" role on the world stage. LINK

The Washington Post's Scott Wilson: " Obama, Iranian President Open Door To Better Relations" President Obama on Tuesday said he will use the remainder of his term to pursue better relations with Iran in the hope of resolving the controversy surrounding its nuclear program, pledging an activist U.S. agenda in the Middle East and beyond despite growing isolationist pressure at home. In a 50-minute address to the U.N. General Assembly, Obama said he will devote his diplomatic efforts in the region to securing an Israeli-Palestinian peace agreement, hopeful that talks now underway through American encouragement may end the long conflict. LINK

The Washington Times' Ben Wolfgang: " Iranian President Brushes Away Obama's Olive Branch At U.N." President Obama used his annual address to the United Nations on Tuesday to say he sees an opening for diplomacy with Iran and would pursue a deal to stop the Islamic republic's pursuit of nuclear weapons - but his words were soon overshadowed by the handshake that wasn't. New Iranian President Hasan Rouhani rejected a White House invitation for a brief meeting with Mr. Obama, an American olive branch designed to move the two countries beyond their adversarial positions and toward peace. The administration later claimed that Iranian officials thought it was "too complicated" to be seen meeting with the U.S. and that the conversation, no matter how short, would have posed political problems back home for Mr. Rouhani. LINK

Bloomberg's Lisa Lere & Margaret: " Obama Says Iran Must Match Words With Verifiable Action" President Barack Obama welcomed overtures from Iran as a chance to diplomatically resolve the confrontation over the Persian Gulf nation's nuclear program, even as Iranian officials told the U.S. that the time isn't right for direct contact between the two countries' leaders. The U.S. is "encouraged" that Iranian President Hassan Rohani was given a mandate in his election to pursue a more moderate course and that may provide a basis for a "meaningful agreement" on the nuclear issue, Obama said in an address to the United Nations in which he also sought to justify the broad U.S. role in world affairs. LINK

The New York Daily News' Kerry Burke and James Warren: " Iranian President Hassan Rouhani Appears To Acknowledge Holocaust As Jewish Leaders Decline Meeting" Iran's new president, Hassan Rouhani, is no Mahmoud Ahmadinejad - he appears to acknowledge the existence of the Holocaust. Amid a media blitz aimed at cutting a new image in stark contrast to that of Iran's former president, Rouhani was asked by CNN's Christiane Amanpour on Tuesday about Ahmadinejad's public denials that Nazi Germany systematically slaughtered Jews. LINK

The Hill's Julian Pecquet: " Seeking Thaw, Obama Seeks Iran Nuke Deal" President Obama formally launched diplomatic talks with Iran on its nuclear program Tuesday despite widespread distrust about that country's intentions. Speaking at the United Nations, Obama announced he had tasked Secretary of State John Kerry with pursuing a nuclear deal with Iran. He also said the White House believes there is a real chance Iran is willing to enter talks that would end its pursuit of nuclear weapons. LINK

OBAMACARE Politico's Jake Sherman and John Bresnahan: " House GOP May Attach Obamacare Delay To CR" The House Republican leadership is seriously considering attaching a one-year delay of Obamacare's individual mandate to the Senate bill to avert a government shutdown, according to senior GOP aides. If House Republicans decide to go this route, it would all but provoke a government shutdown, since Senate Democrats might not even schedule a vote on a bill that includes that provision, Senate leadership staffers say. LINK

The Hill's Niall Stanage: " Clintons Join Obama To Defend Health Law" Former President Bill Clinton and President Obama were welcomed to a "conversation" about ObamaCare on Tuesday by former secretary of State Hillary Clinton. The unusual event briefly brought together the last, current and possibly future Democratic presidents -and highlighted how much a successful implementation of the law would benefit not just Obama but Hillary Clinton, if the 2016 Democratic frontrunner chooses to run. LINK

The Los Angeles Times' Kathleen Hennessey: " With Bill Clinton At His Side, Obama Sells Healthcare Law" President Obama accused foes of his healthcare law of trying to sabotage it for political gain, saying opposition has become a "litmus test" for Republicans. The result, Obama said Tuesday evening, is that the law is mired in partisan politics in state legislatures and Congress. "Normally this would be pretty straightforward. A lot of people don't have health insurance, a lot of people realize they should get health insurance," he said. "But, let's face it, it's been a little political, this whole Obamacare thing." LINK

USA Today's Martha T. Moore: " Obama, Bill Clinton Team Up On Health Care Push" If "Obamacare" is so great, President Obama asked Tuesday, why do polls show it is so unpopular? In a nearly hour-long pitch for his signature legislative achievement, Obama and his health care ally, former president Bill Clinton, said that mandated health insurance would improve the economy and torpedo the budget deficit, all for the cost, Obama said, of a monthly cellphone bill. LINK

ABC NEWS VIDEO " Obama Pushes UN to Confront Chemical, Nuclear Weapons" LINK

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