raqi Prime Minister Haider Abadi waved his national flag in a devastated Mosul last week and with good reason. He was celebrating the hard-fought victory of his U.S.-supported troops over the stubborn Islamic State terrorists who held Iraq's third-largest city for more than three years. But Abadi was candid about the challenge going forward: "We have another mission ahead of us — to create stability."

Bringing peace to a region fraught with tension and fear, riven by spasms of score-settling violence and angry rivalries, is the toughest victory to achieve. Mosul was the great prize for the Islamic State's twisted dream of an ISIS-controlled territory. It took nine months, the lives of perhaps 1,000 Iraqi troops and too many civilian casualties to regain it. The recapture of Mosul is terrific news. But what happens after the battle will define whether extremism has won or lost.

This next chapter cannot succeed with U.S. military advisers and airstrikes. It demands that the "soft power" of the State Department and the United Nations be brought to bear, coupled with relentless, on-the-ground mediation between rival factions by American advisers and Iraqi civil society groups. Too many things can go wrong too quickly in the ashes of Mosul, where 80% of its once densely populated western sector lies in ruin.

Bodies of handcuffed prisoners, beheaded or shot, are already showing up in human rights reports and Internet videos. The atrocities, of course, pale in comparison to the sins of ISIS, which used women and children as shields and gunned down families trying to flee embattled neighborhoods. Islamic fighters blew up the 800-year-old Great Mosque of Nuri, where leader Abu Bakr al-Baghdadi declared creation of the ISIS caliphate in 2014. But for Abadi's government to demonstrate legitimacy, it must set a far higher standard.

The prime minister has won high marks for even-handed helmsmanship in Shiite Muslim-majority Iraq, particularly in the wake of predecessor Nouri Maliki, whose persecution of Iraq's minority Sunni population created fertile ground for the Islamic State's incursions. Abadi has added Kurdish and Sunni leaders to his cabinet, opened discussions with the Sunni community and decentralized power to the provinces, all to the better.

ANOTHER VIEW

But Mosul and the surrounding Nineveh Province remain filled with teeming, vicious cross-currents.  As hundreds of thousands of displaced Mosul residents bake in desert-tent displacement camps in 110-degree heat, and city municipal leaders work to clear roadways and reconnect power, everyone is finding someone to hate.

Sunnis oppose Shiites. Turkish proxies resist Iranian-backed Shiite militias. Groups favoring a unified region quarrel with those who want division. Kurds seek autonomy. There's even fracturing within tribes and families, especially between Sunni Arabs who shunned ISIS and those who did not, according to Institute of Peace executive Sarhang Hamasaeed.

Violence is never far away. "There are so many triggers," he says.

Similar challenges await coalition leaders once they succeed in liberating the Islamic State's de facto capital of Raqqa in war-torn Syria. In Mosul, American and U.N. diplomats must push for mediation and compromise; encourage and fund local non-government groups that quell simmering disputes; and press for free and inclusive elections in September for the province and early next year for parliament. Too much is at stake, including the chance that scattering remnants of ISIS could mount a comeback.

America blundered badly in 2003 when it invaded Iraq based on false premises about weapons of mass destruction. It blundered again by withdrawing all U.S. troops in 2011, creating a vacuum that ISIS filled. Blundering a third time would be unforgivable.

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