President Obama arrives to chair the Countering Violent Extremism leaders’ summit at the United Nations. (Andrew Harnick/The Associated Press)

President Obama came here this week to argue that the era of global superpower rivalry should be relegated to the past, and that only broad, international coalitions can tackle the dangers facing an interconnected world.

But his optimistic, multilateralist vision ran into the harsh reality of world events: not just sharp disagreement with Russian President Vladimir Putin over how to resolve the brutal civil war in Syria, but also news from Afghanistan that the Taliban had taken control of the strategically important northern city of Kunduz.

At each United Nations stop, the president’s words and gestures reflected his determination to change the old calculus. On Tuesday, he rose alongside Cuban President Raúl Castro, grasping his hand with a wide grin to show that renewed diplomatic relations between the two countries were well underway. During a U.N. luncheon Monday, he shook hands with Iran’s foreign minister, Mohammad Javad Zarif, the first such contact between a U.S. president and any high-ranking Iranian official since the 1979 Islamic revolution.

Speaking to the General Assembly on Monday, Obama pressed the point that neither force nor anti-democratic tactics could help countries chart a stable future.

“Just as force alone cannot impose order internationally, I believe in my core that repression cannot forge the social cohesion for nations to succeed,” he said. “The history of the last two decades proves that in today’s world, dictatorships are unstable. The strongmen of today become the spark of revolution tomorrow.”

Stewart Patrick, who directs the program on International Institutions and Global Governance at the Council on Foreign Relations, said Obama has been frustrated by the resurgence of great-power politics, such as clashes with Russia and China. “I think he’s been a bit sobered up in recent years,” Patrick said.“It’s almost as if there are two games going on, and the question is whether the two games can go on simultaneously.”

In certain areas, Obama’s approach has clearly gained traction. In addition to the diplomatic advances with Iran and Cuba, the summit on peacekeeping that the United States convened Monday generated pledges from 52 countries that included commitments of roughly 40,000 new troops and significant new resources such as 40 helicopters and 10 field hospitals.

Bruce Jones, vice president and director of foreign policy at the Brookings Institution, called it “breakthrough progress” that showed how America had spurred “a race to the top” among players — such as the Chinese — who want to show they’re invested in the world more broadly. China said it would establish an 8,000-person peacekeeping standby force and provide $1 billion over the next 10 years to a U.N. “peace and developing fund.”

“These are big shifts, and that’s a hundred percent due to President Obama,” Jones said, adding that climate change and sustainable development are other examples of where the president has mobilized meaningful global action.

But in the Middle East, Obama’s efforts have collided with Russia’s determination to back Syrian President Bashar al-Assad. Equally important, the president’s reluctance to get entangled in another protracted military fight overseas has limited the extent to which the United States has been able to counter Islamic State extremists there. “The result is a swirling race to the bottom,” Jones said.

White House officials pointed out that a handful of countries joined their campaign against the Islamic State this week, bringing the coalition’s total number to 65. France also agreed to conduct military strikes inside Syria for the first time.

But for the most part, the discussion over how to tackle the global terrorist threat seemed to mirror previous ones, such as the summit Obama hosted in Washington in February. On Tuesday, the president chaired a Countering Violent Extremism leaders’ summit, and he reiterated the points he has tried to convey to domestic and international audiences: that the world must counter terrorists’ appeal on social media and by providing responsive government.

“I’ve said this before — when human rights are denied and citizens have no opportunity to redress their grievances peacefully, it feeds terrorist propaganda that justifies violence,” the president said at one point.

The president also reiterated during the summit that he is willing to work with Iran and Russia to bring peace to Syria. Monday marked Putin’s and Obama’s longest conversation in two years, but they remain far apart on how to beat back the Islamic State in both Syria and Iraq.

Asked whether the U.S. reluctance to escalate its military involvement there had opened the door for Russia to step in, White House press secretary Josh Earnest said the president had no interest in the go-it-alone approach that powerful countries had pursued in the past.

“It’s the president’s view that the United States is acting from a position of strength when we mobilize the international community, even lead the international community, in responding to difficult international crises,” Earnest said. “And We’ve seen, at the risk of understating it, the downsides of unilateral U.S. military commitment to conflicts in the Middle East. And in fact the U.S., and even the region, is still paying the price from some of those ill-advised decisions.”

What is still unclear is how many more converts Obama can win before he leaves office.

“Unfortunately for the United States, there are a number of countries standing on the sidelines in this debate,” Patrick said, noting that Russia and China have some appeal for many unaligned countries. “They’re looking at these authoritarian countries with strong leaders, and they’re also looking at the hash of things the United States and some of their allies have made in much of the Mideast and North Africa.”

In contrast to 2009, when Obama came to the United Nations as the anti-George W. Bush, the response to his speech this week was relatively muted. His line about restoring relations with Cuba got his biggest round of applause; the section on rejecting force as a way to settle international disputes was received largely in silence.

But there is no question that Obama — whether through his direct intervention, or refusal to intervene, overseas — continues to shape the contours of world affairs. Earnest noted that General Assembly Hall was packed when Obama took the podium Monday.

“And I think that says something about the president, but it also says something about the United States,” Earnest said. “The world is there to listen and is eager to hear about our country’s priorities and our values. And that’s an indication that the United States continues to be the country that the international community looks to when confronting significant international crises.”