It was Barack Obama's big moment. He made his case to the world that the so-called "Islamic State" (IS) must be destroyed. It was just part of a day's diplomacy that one expert sees as a "turning point."
Just four months after setting out a new vision of foreign policy for an era beyond the wars in Iraq and Afghanistan, now Obama stood before a changed world and told it: "We come together at a crossroads between war and peace."
Meanwhile, thousands of kilometers away, US war planes continued air strikes against IS targets in both Iraq and Syria.
The language of force
Obama portrayed those strikes as unavoidable: "The only language understood by killers like this is the language of force."
It was a striking shift from the cautious language of just a few weeks ago, when Obama would talk in terms of "pushing back" or "taking the fight to" IS.
Frenchman Herve Gourdel was beheaded Wednesday by the Algerian, IS-linked Jund al-Khalifa terror group
Now his tone went beyond even the latest formulation of "degrading and destroying" the group, saying, "There can be no reasoning - no negotiation - with this brand of evil."
But one theme from his May address at the West Point Military Academy remained: the importance of not acting alone.
"The United States of America will work with a broad coalition to dismantle this network of death," Obama said. "Today, I ask the world to join in this effort."
At present count the White House says it has more than 40 partners taking part in the coalition against IS in Iraq. As Wednesday progressed, one more looked likely to join the air strikes in that country as British Prime Minister David Cameron tweeted that he would recall parliament to debate such a move and told the General Assembly that Iran could be "part of the solution." And five Gulf states are playing a role in the strikes in Syria. As Obama stressed: "In this effort, we do not act alone."
This linked to a pivotal sentence in Obama's speech, what he called "a central question of our global age: whether we will solve our problems together, in a spirit of mutual interests and mutual respect, or whether we descend into destructive rivalries of the past."
For Tom Wright, a strategy analyst at the independent Brookings Institution in Washington, this was a revealing moment.
He told DW, "In previous speeches, he seemed to think that it was inevitable that the answer to this question would be cooperation. In this speech, he appears worried the answer is old rivalries. I think he is right now and was mistaken then."
For Obama, those "old rivalries" are ever-present in the Middle East. He called for a "broader negotiation in which major powers address their differences directly, honestly, and peacefully across the table from one another, rather than through gun-wielding proxies."
Growing risks in the Asia-Pacific - where China's territorial disputes with its neighbors are causing growing alarm - earned just a glancing mention in Obama's speech, with the president demanding "that all nations abide by the rules of the road, and resolve their territorial disputes peacefully, consistent with international law."
But nowhere is that risk of a return to "old rivalries" greater than in Eastern Europe, where Obama said Russian aggression "recalls the days when large nations trampled small ones in pursuit of territorial ambition."
Alongside IS, the crisis in Ukraine formed the second major plank of his speech. He presented it as more than a tug-of war over one country's future - as a challenge to the entire post-war order that followed the devastation of 1939-1945.
Tom Wright was heartened by these remarks. "In previous speeches, he has tended to downplay what happened in Ukraine. But he did not do that here."
Brett Schaefer of the conservative Heritage Foundation, however, wasn't convinced. In a recent piece he wrote that Obama "asked Russia to change direction, but did not call on the UN to do anything - an implicit admission that the international system was incapable of action on the matter."
Despite his condemnation of Russia for posing a threat to global cooperation, Obama won Moscow's backing for one element of his push against IS and terrorism more generally. It was the second part of the US president's big day: chairing a special meeting of the UN Security Council and winning unanimous support for a resolution on foreign fighters taking part in the wars in Iraq and Syria, as well as other conflicts.
In a brisk statement, Russia's foreign minister, Sergei Lavrov, remarked on the vote as reaffirming the ability of the UN Security Council - deadlocked for so long on Syria - to agree on big issues. This just a day after he condemned the US for launching its air strikes against IS in Syria without Damascus's express permission, saying, "Attempts to pursue geopolitical objectives and violations of the sovereignty of states in the region can only aggravate tensions and further serve to destabilize the situation."
The Security Council asked countries to disallow nationals from fighting with or funding terror groups abroad
It is not just Moscow that has doubts over the legality of the air strikes in Syria. The New York Times ran a prominent editorial on Wednesday registering dismay over Obama's "wrong turn," arguing that the UN Security Council should vote on the issue.
Instead, the White House is arguing that it is acting in the defense of Iraq, which has requested its help against the IS threat, and that Syria's government is incapable of acting, having lost control of its own territory.
It's a legal argument dismissed by some critics as "contorted." But Tom Wright says the US won't take this case to the Security Council. Russia, he says, would inevitably link its support to conditions the US could not accept - such as cooperating with the Assad regime. For now, the White House is insisting it will not work with Assad, arguing that he has lost all legitimacy in three years of civil war.
A year ago, Barack Obama told the UN General Assembly that his country was "shifting away from a perpetual war footing." This year, some see the risk of it shifting back in the opposite direction.
For Tom Wright, Obama's new robustness is, however, a positive.
"We are returning to an older age of rivalries, and the challenge is how to arrest that or deal with it."