As we did in Iraq with the 2006 “Anbar Awakening,” the counterinsurgency operation that dislodged Al Qaeda from its stronghold in that Iraqi province, we and our allies must empower viable Sunni leaders, including tribal authorities who prize their existing social structures. No doubt, this will involve former Iraqi and Syrian Baath Party officials; and there may still be some moderate Syrian opposition leaders. All are preferable to the Islamist extremists.

The Arab monarchies like Saudi Arabia must not only fund much of the new state’s early needs, but also ensure its stability and resistance to radical forces. Once, we might have declared a Jordanian “protectorate” in an American “sphere of influence”; for now, a new state will do.

This Sunni state proposal differs sharply from the vision of the Russian-Iranian axis and its proxies (Hezbollah, Mr. Assad and Tehran-backed Baghdad). Their aim of restoring Iraqi and Syrian governments to their former borders is a goal fundamentally contrary to American, Israeli and friendly Arab state interests. Notions, therefore, of an American-Russian coalition against the Islamic State are as undesirable as they are glib.

In Syria, Moscow wants to dominate the regime (with or without Mr. Assad) and safeguard Russia’s Tartus naval base and its new Latakia air base. Tehran wants a continuing Alawite supremacy, with full protection for Hezbollah in Lebanon and Syria.

As for Iraq, Russia and Iran want the Sunni territories returned to Baghdad’s control, reinforcing Iran’s regional influence. They may wish for the same in Kurdistan, but they lack the capability there.

Sunnis today support the Islamic State for many of the same reasons they once supported Al Qaeda in Iraq — as a bulwark against being ruled by Tehran via Baghdad. Telling these Sunni people that their reward for rising against the Islamic State in Syria and Iraq will be to put them back in thrall to Mr. Assad and his ilk, or to Shiite-dominated Baghdad, will simply intensify their support for the jihadists. Why would they switch sides?

This is why, after destroying the Islamic State, America should pursue the far-reaching goal of creating a new Sunni state. Though difficult in the near term, over time this is more conducive to regional order and stability.