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ERBIL, Iraq — A military push to recapture Mosul, Iraq’s second largest city, and the rest of Nineveh Province from the Islamic State is expected soon. Unfortunately, even if the campaign is successful, the liberation of Mosul will not stabilize the country. Nor will conquest resolve the underlying conditions that originally fueled the extremist insurgency.

Instead, the legacy of the Islamic State, or ISIS, will endure. Its rise and fall have altered the country’s society and politics in irreversible ways that threaten future cycles of conflict. Throughout history, victorious wars have often forged national identities, expanded state power and helped centralize political authority. But the war against the Islamic State is having the opposite effect: fragmentation.

In parts of Iraq recaptured from the militants where I’ve traveled, signs of any central authority are nonexistent. Instead, what has emerged from the conflict is a complex patchwork of ethnic, tribal and religious militias that claim fief over particular territories.

This was the case in liberated parts of Sinjar, where the massacre of Yazidis, a religious minority, perpetrated by the Islamic State with local Sunni collaborators compelled the United States to intervene militarily in 2014. Now the remaining Yazidi community is divided and militarized, with each militia backed by a different Kurdish faction, and each Kurdish faction in turn backed by a different regional power.

In Nineveh Province, the social fabric that long reflected the coexistence of diverse groups seems permanently damaged.

“ISIS changed everything,” one Yazidi man told me. “We can never trust Arabs again.”

I heard the same message from members of other minority groups. Each now demands political autonomy. In Iraq’s northern region, the war has encouraged Kurdish nationalist aspirations to crystallize into urgent demands for statehood. It’s difficult to find anyone who feels they belong to the Iraqi nation.

In part, the Islamic State was able to expand so rapidly in 2014 because it provided an opportunistic means for groups to settle longstanding scores. At no other time has sectarianism in Iraq been so hardened, with communities even of the same sect fragmented.

Sunni tribes have fractured at a local, even village, level, with some grabbing power by joining the Islamic State, while others fled or resisted. In Anbar Province, for instance, more than 100 men now claim to be a sheikh, or leader, of a tribe.

The Baghdad government’s writ does not apply in most of Iraq. The administration’s weak authority has forced the prime minister, Haider al-Abadi, to rely on dozens of Shiite militias to shore up national security. Mr. Abadi has tried to integrate these forces to bring them under his control, but the process has created parallel command structures within the security apparatus.

In practice, the militias answer to a murky network of patronage and loyalties divided among different political parties, religious clerics and external patrons. It’s hard to tell where the militias end and the state begins.

The American experience in Iraq has been plagued by a series of false assumptions, misplaced confidence and poor foresight. In the latest manifestation, since 2014, the White House has wrongly prioritized the narrow, short-term military objective of defeating the Islamic State.

The push to retake Mosul is not simply a case of the Iraqi Army against the Islamic State; instead, an array of armed groups — each driven by its own parochial interests — are set to wage war there. This alone should give American policy makers pause, because of the threat this situation poses to reconstruction and post-conflict stability.

To offset this problem, the United States hopes to broker preliminary agreements between the combatant groups in the Mosul campaign. So far, these efforts have yielded little. For example, there is no consensus on how to determine which civilians joined the Islamic State willingly, which cooperated for protection, or which were not involved at all. There is no protocol on how to prevent acts of retribution between communities, and no guarantee that the militias the United States wants excluded from the campaign would remain on the sidelines.

In the absence of any effective chain of command, it seems unlikely that rules of engagement will be adhered to. With no one to enforce compliance and accountability, parties are more likely to cheat on previous commitments. One of the few beliefs that Iraqis across the sectarian divide share is that the United States will soon disengage completely from their country.

The very diversity of Nineveh’s population makes it more vulnerable than Anbar, which is mainly Sunni Arab, to being carved up along ethnic and religious lines. The only militias’ collective interest — in the defeat of the Islamic State — will end when the province is retaken. For many, fighting the Islamic State is not about saving the nation or the state; it’s an opportunity to reap the political spoils of conquest.

Among the groups competing for those rewards are: Sunni Arab tribal militias looking to expand control over territory ahead of the next provincial elections; Shiite Turkmen militias aiming to cleanse Sunni Turkmens from the area; Shiite Arab militias seeking a bigger say in government; and Kurdish groups wishing to consolidate control over disputed territories. Behind all these is a prime minister who needs a victory to strengthen his weak hand in Baghdad. And behind him are Turkey and Iran, both maneuvering their armed proxies to extend their influence.

In the face of these forces, Nineveh’s provincial government, which has been in exile for over two years, does not have the capacity to re-establish its authority. A new governor was appointed last year, but he commands neither a political party nor a solid coalition of allies.

American policy makers would be foolish to hope they could control such a complex environment of conflicting interests. Nor should they rely on these armed groups’ disarming after the Islamic State is defeated. Given this unpromising picture, President Obama would be wise to postpone the military campaign. Any rushed victory would most likely prove pyrrhic — further fragmenting the civil-war-ravaged country and pushing it toward a new phase of armed sectarian politics.

Instead, Mr. Obama should devote his remaining time in office to pressure the Abadi government to build a single military force that is tailored to liberate the rest of Nineveh. That would be an army that reflected the province’s demographics and tribes and had effectively integrated its constituent militia groups under a unified national command.

Mr. Obama has helped degrade the Islamic State in Iraq. But defeating it must not come at the risk of a new, and perhaps more deadly, civil war.