President Obama speaks at the United Nations on Sept. 27. (Andrew Harnik/AP)

President Obama arrived at the United Nations on Sunday arguing that in a chaotic and dangerous world, diplomatic action, and not military force, represents the best way of tackling the most daunting global challenges.

“Today, we set aside the skepticism, and we lift up the hope that is available to us through collective action,” Obama told his fellow leaders gathered in General Assembly Hall, with its lime-green carpeting and abstract wall murals. “Despite the cruelties of our world and the ravages of disease, millions of lives can be saved if we are focused, and if we work together.”

Even in the face of ongoing crises — including armed clashes in Syria, Iraq and Ukraine, as well as the pervasive threat of terrorist activity by the Islamic State and other extremists — this is a moment of modest triumph for Obama.

This year’s General Assembly session of the U.N. illustrates the extent to which Obama’s foreign policy approach has reshaped the global landscape over the past seven years, with historic deals with Iran and Cuba as well as a big climate agreement with China. But the flow of Islamist terrorists into Syria and Iraq and the resulting flood of refugees out of the region can often mute the sheen of those breakthroughs.

The halls of the U.N., which is celebrating its 70th anniversary this year, bear testament to how much has changed since Obama came here in 2009, declaring the world “must embrace a new era of engagement based on mutual interest and mutual respect.”

Iranian President Hassan Rouhani mingled with other leaders and members of the media, basking in this year’s negotiated settlement over Tehran’s nuclear program. Obama will hold a one-on-one meeting Tuesday with Cuban President Raúl Castro, the first time the two men have met on U.S. soil since their countries restored diplomatic ties in December.

On Sunday, the president endorsed new Sustainable Development Goals, a sweeping set of objectives aimed at eradicating poverty within the next 15 years while simultaneously protecting the planet. But even as that event exemplified the lofty ambitions he frequently invokes — global cooperation on an affirmative, shared agenda — U.S. and Russian officials clashed behind the scenes over their different ideas about how to end the ongoing conflicts in Syria and Ukraine.

American University international politics professor David Bosco described this week’s gathering as “a post-breakthrough General Assembly,” but also one in which the U.N. Security Council is no longer an easy place to mobilize an alliance among the major powers.

“With Russia, the deterioration has really happened on Obama’s watch,” Bosco said. “Because of the difficulty in the relationship with Russia, the Security Council has become more difficult terrain for the United States than when Obama took office.”

While Obama has continued to use military force to target specific terrorists overseas and has assembled a multinational coalition to conduct a campaign against the Islamic State in Iraq and Syria, he has opted to employ diplomatic sanctions in response to Russian aggression.

On Monday, Obama will chair a summit on international peacekeeping, another example of how the United States has sought to achieve some of its goals without putting its soldiers in harm’s way. There are about 100,000 troops deployed around the world under U.N. blue helmets in roughly 16 missions, and the United States is the largest financial contributor to that effort. But the vast majority of U.N. peacekeepers come from developing countries: There are roughly 40 U.S. military personnel and nearly 50 U.S. police and corrections officers now serving in peacekeeping operations in Haiti, South Sudan and Liberia.

Michael Ignatieff, a professor at Harvard’s Kennedy School, said the president recognizes “multilateralism is an extremely good bargain for a superpower. . . . You can exert power and influence, without taking full responsibility.”

“He’s a multilateralist because he believes the United States can’t do it all and has to leverage alliances with other countries,” Ignatieff said.

Speaking to reporters last week, White House deputy security adviser Ben Rhodes said that while the administration favors non-military solutions in many instances, it will continue to push back against Russia’s annexation of Crimea and support for separatists in southeastern Ukraine.

Referring to the speech Obama will deliver Monday at the U.N., Rhodes said the president will “be underscoring the importance . . . of there being a rules-based approach to solving problems.”

On Sunday, the focus was on the most aspirational of missions: addressing deprivation in the world’s poorest regions while also ensuring gender equality, accountable governmental institutions, environmental sustainabilty and universal access to energy as well as justice.

The session began with a video listing the U.N.’s Sustainable Development Goals, which include 17 broad objectives and 169 different targets within those categories. While the presentation featured men and women from different ethnic and racial backgrounds, speaking multiple languages, it was most notable for the number of global celebrities it featured, including theoretical physicist Stephen Hawking, conservationist Jane Goodall, actor Daniel Craig and singer Stevie Wonder.

The goals are the successor to the Millennium Development Goals, adopted in 2000, which were more narrowly focused on economic and public health challenges worldwide. Manish Bapna, executive vice president of the World Resources Institute, said the new targets “are much more transformative” and arose from a more inclusive negotiation involving all 193 U.N. member countries as well as civil society and the private sector.

Obama pledged he would work “as long as I am president, and well after I’m done being president,” to achieve the goals outlined by the initiative. And while the president did not attend a U.N. leaders’ lunch focused on climate change — opting instead to have lunch with his sister Auma in his hotel — he praised the idea that “the world’s poorest people will bear the heaviest burden — from rising seas and more intense droughts, shortages of water and food.”

Felipe Calderón, the former president of Mexico who now co-chairs the Global Commission on the Economy and Climate, said that even though the goals can seem abstract, they “are very useful” because countries align their policies to try to achieve them.

Bapna noted that the United States has already rolled out policies on cutting food waste and expanding legal aid that mesh with the goals; Colombia has created an inter-ministerial commission to pursue the targets.

Oxfam America president Raymond C. Offenheiser said “the broader challenge” the world faces “is not whether or not the Sustainable Development Goals are the right goals but whether the U.S. and other countries have the political will to make them happen.”

Obama closed his speech by reading from a letter from a ­15-year-old Tanzanian girl, Eva Tolage. In it, she said she dreams of being educated even though she does not have regular access to clean water and electricity.

“What will you commit to doing to help young people actually lead development?” Tolage asked in her letter.

“And so today, I say to Eva and hundreds of millions — billions — like her: We see you,” the president said. “We hear you.”