ERBIL, Iraq — THE Islamic State continues to control a huge section of Syria. But in Iraq, its advance has stalled. While Shiite militias and their Iranian allies fight the Islamic State ferociously, the Kurds have held a 640-mile front against the Islamic State’s advance. Their steadfastness should prompt America to rethink its alliances and interests in the region and to deepen its relationship with the Kurds — who are sometimes described as the world’s largest stateless nation.

Last week, the Sunni town of Tikrit (Saddam Hussein’s hometown) fell to largely Shiite forces from Iraq, backed by Iran. An offensive to retake Mosul, Iraq’s second largest city and the heart of Arab Sunni nationalism, is now within reach. The Kurds plan to enter eastern Mosul, where many Kurds lived before the Islamic State seized the city in June, but they say that moderate Arab Sunnis must lead the effort to retake the rest of the city — not Baghdad’s predominantly Shiite forces or the Iranian-backed Shiite militias. The Kurds point out that it was grievances against Shiite rule that helped drive Sunni support for the Islamic State in the first place.

Together with Lydia Wilson and Hoshang Waziri, our colleagues at Artis, a nonprofit group that uses social science research to resolve intergroup violence, we found that the Kurds demonstrate a will to fight that matches the Islamic State’s. The United States needs to help them win.

In Kirkuk last week, where only a narrow canal separates Kurdish and Islamic State forces, we talked to three captured Islamic State fighters, and to their captors: Gen. Sarhad Qadir, the city’s Kurdish police chief, and his deputy, Col. Gazi Ali Rashid.

General Qadir, who lost a brother in earlier fighting, has been wounded 14 times in battles with Sunni militants, most recently in a suicide attack on Tuesday. The Islamic State recently paraded Colonel Rashid’s brother in a cage, along with other Kurds captured in a large-scale offensive that stalled in late January. Arab Sunni tribes have been trying to negotiate a prisoner exchange to signal to the Kurds that they are not all aligned with the Islamic State, but Colonel Rashid has no hope. “I know my brother will die,” he told us shortly before he was severely wounded on Tuesday.

The Islamic State prisoners most likely will be executed for having committed assassinations and deadly car bombings. The three are in their early 20s; two have wives and young children. None finished elementary school. They recounted growing up in the failed Iraqi state during the last decade: a hellish world of guerrilla war, disrupted families, constant fear and utter lack of hope. They see Iran and the Shiites as their greatest enemy but they also believe that America allowed them to oppress the Arab Sunni minority for the sake of majority rule.

When we asked the prisoners “What is Islam?” they answered “my life.” Yet it was clear that they knew little about the Quran, or Islamic history, other than what they’d heard from Al Qaeda and Islamic State propaganda. For them, the cause of religion is fused with the vision of a caliphate — a joining of political and religious rule — that kills or subjugates any nonbeliever.

The Kurds’ commitment to Islam is matched by their commitment to national identity; theirs is a more open-minded version of Islam. They have defended Yazidis and Christians, as well as Arab Sunnis, who make up the bulk of the more than one million displaced persons in Iraqi Kurdistan.

But perhaps what most reveals commitment by the Kurds is how they hold the line with so little material assistance.

On the night of Jan. 30, the Islamic State used the cover of fog to attack a Kurdish battalion near the town of Mahmour. Seven Kurds were killed immediately. Their colleagues said that if they had had night-vision goggles — or better yet, thermal-imaging scopes to also detect vehicles — all would most likely be alive. When we gave them a gift of our small, store-bought binoculars with which we had been watching Islamic State movements less than one mile away, they expressed deep gratitude. As we left, a mine went off as they moved earth to make a defensive wall, for there is no demining equipment.

To be sure, coalition airstrikes have prevented Islamic State forces from deploying heavy artillery to break Kurdish lines, although Gen. Sirwan Barzani, who commands the main front between Erbil and Mosul, told us that a Pentagon lawyer must approve every strike (a policy intended to minimize chances of civilian casualties from drone attacks). Sometimes, that approval comes too late.

With its big guns vulnerable to air attack, the Islamic State adapts its tactics, piercing Kurdish lines with suicide attacks in primitively armored vehicles. One Kurdish commando near the Mosul Dam showed us, on his smartphone, a video of the approach of a steel-hardened vehicle. No amount of rifle fire or rocket-propelled grenades could stop the attack, which killed 23 and wounded 40.

Yet the United States insists that the Kurds obtain permission, grudging and often denied, from the central government in Baghdad for essential equipment to counter these and better weapons that the Islamic State seized from the Syrian and Iraqi Armies.

Meanwhile, the Islamic State won’t quit. Their wounded fighters often booby trap their bodies rather than be captured, and face down fire to recover dead comrades’ bodies. The leaders they call emirs, who are chosen because of their religious devotion and fearless effectiveness, and their foreign fighters, are especially fierce. The Westerners often die in suicide attacks; seasoned fighters from North Africa and the Middle East, and particularly from former parts of the Soviet Union (like Chechnya, Uzbekistan, Dagestan), are prominent as operational leaders and snipers. Foreign fighters return to their countries only if they escape or are sent home, because the punishment for defection is death.

Local Syrians and Iraqis conscripted to fight for the Islamic State, in contrast, are not totally committed. In one conversation picked up by a Kurdish walkie-talkie, a fighter with a local accent asked for help: “My brother has been killed. I am surrounded. Help me take his body away.” The reply: “Perfect, you will join him soon in Paradise.” The fighter retorted: “Come for me. This Paradise, I don’t want.”

The Islamic State will say to a local sheikh: “Give us 20 young men or we loot your village.” To a father with three sons, they will say: “Give us one or we take your daughter as a bride for our men.” One girl of 15 told how she was “married” and “divorced” 15 times in a single night to a troop of Islamic State fighters (under some readings of Shariah law, “divorce” is as easy as repeating “I divorce you” three times, which makes it easy to cast rape as marriage). In the face of such brutality, wavering supporters of the Islamic State could well rally to an Arab Sunni force allied with the Kurds. That is a prospect the United States, which fears leaving the fight mainly to Iran and its allies, should welcome.

As we said goodbye at the front, a young Kurdish sniper promised us she would never abandon her comrades or their cause. Will the United States deny her people the means to counter the Islamic State — for the sake of upholding the costly illusion of an Iraqi nation-state, devised from three Ottoman provinces to fit British imperial desires but now hopelessly fragmented?

Kurdish leaders say they would accept a federated Iraqi state if they were given autonomy in political, economic and security matters. The United States should have agreed to do this long ago; it’s not too late to do so now. If America does not, Iraqi Kurdistan will most likely declare itself an independent state, which Turkey, Iran and Syria will move forcefully to stop, for fear that their own Kurdish populations will try to join it.

The United States must help the Kurds translate their bravery into a true ability to defeat the Islamic State. They are America’s most reliable friends on the ground, and should be treated as such.