This is how a Nobel Peace Prize laureate goes to war.

He smiles warmly at the members of the U.N. General Assembly. He mentions his grandmother’s village in Kenya and notes that “Islam teaches peace.” He admits his country’s own flaws, praises “the path of diplomacy and peace,” and asserts that lasting gains cannot be “won at the barrel of a gun.”

Also, he wades a good 19 minutes into his 40-minute speech (the official time limit is 15 minutes) before getting to the nub of the matter: “The terrorist group known as ISIL must be degraded and ultimately destroyed.”

“In the most horrific crimes imaginable, innocent human beings have been beheaded, with videos of the atrocity distributed to shock the conscience of the world,” he says. “No god condones this terror. No grievance justifies these actions. There can be no reasoning, no negotiation, with this brand of evil. The only language understood by killers like this is the language of force. So the United States of America will work with a broad coalition to dismantle this network of death.”

Network of Death! A linguistic heir to George W. Bush’s Axis of Evil, perchance? “Those who have joined ISIL should leave the battlefield while they can,” the peacemaker threatens.

This is a different Obama from the one who spoke in Cairo five years ago, urging a new era in relations between America and the Muslim world. Though similar themes appeared in both addresses, the 2014 Obama was more demanding of the Muslim world — and less apologetic about America’s role — as he lectured Muslim leaders to make a serious fight against extremists.

In the 2009 speech, Obama invoked the “Holy Koran” five times and asserted that “any world order that elevates one nation or group of people over another will inevitably fail.” He spoke out against the U.S. use of torture and said he would close the Guantanamo Bay prison. (He didn’t.) He spoke of the “intolerable” situation faced by Palestinians and called for a stop to Israeli settlements.

“The enduring faith of over a billion people is so much bigger than the narrow hatred of a few,” the new president said. “Islam is not part of the problem in combating violent extremism — it is an important part of promoting peace.”

On Wednesday, the second-term president went relatively easy on Israel, instead telling Arab countries to stop using the conflict “as an excuse to distract people from problems at home.”

Obama was stern in his instructions for the Muslims: “It is time for the world, especially in Muslim communities, to explicitly, forcefully and consistently reject the ideology of organizations like al-Qaeda and ISIL,” also known as the Islamic State. He went on at some length about the intolerance of clerics who preach hate and the “hypocrisy” of those who fund terrorism.

The president gave the world homework, instructing them to report back next year on “concrete steps that we have taken to counter extremist ideologies.” And he instructed Arab nations to “acknowledge the destruction wrought by proxy wars and terror campaigns between Sunni and Shia across the Middle East.”

Obama, against the familiar green-marble backdrop in midtown Manhattan, gave Russia a sharp but brief slap, decrying its “might makes right” invasion of Ukraine. He took the delegates on a brief world tour — across the Pacific, to Iran and into Africa’s Ebola crisis — before settling in the Middle East, where he used language similar to his predecessor’s.

“In this century, we have faced a more lethal and ideological brand of terrorists who have perverted one of the world’s great religions,” he said. “With access to technology that allows small groups to do great harm, they have embraced a nightmarish vision that would divide the world into adherents and infidels, killing as many innocent civilians as possible, employing the most brutal methods.”

In the end, he pulled back from his Bush imitation by mentioning this summer’s racial strife in Ferguson, Mo. “What you see in America is a country that has steadily worked to address our problems,” he told the world leaders. “. . . America is not the same as it was” even a decade ago, “because we address our differences in the open space of democracy with respect for the rule of law, with a place for people of every race and every religion.”

“After nearly six years as president,” Obama said, “I believe that this promise can help light the world.”

It was a powerful expression of American exceptionalism — rooted not in power but in justice — and an artful way for a man of peace to make the case for conflict.

Twitter: @Milbank

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