By David Ignatius | The Washington Post

MOUNT BATMA, Iraq — From the heights here, you have a panoramic view of the strategic territory west of Mosul that Kurdish peshmerga fighters, supported by U.S. warplanes, have won back from the Islamic State over the past month. The main road linking Mosul with the Syrian border has been cut and nearly 100 square miles have been liberated.

You can see the smoke of rockets fired from distant Islamic State positions and hear the thud of explosions. “They don’t have a target, they just fire to demonstrate to us that they’re still here,” says Gen. Khalaf Ganjo, a Kurdish commander in the region. He’s a big, jowly man who walks with a limp because of a grenade wound suffered in last month’s offensive near here.

A tour with Kurdish commanders this week demonstrated that the U.S.-backed campaign against the Islamic State, or ISIS, as it is called here, is making slow, steady progress. We traveled along roads that a few weeks ago were held by Islamic State extremists; we passed scores of Kurdish houses that had been dynamited by the jihadists as they retreated; we even drove along the top of the Mosul Dam, a strategic prize that was liberated last August in the first big victory of the campaign.

At the Kurdish forward command headquarters, Masrour Barzani, who oversees intelligence, explains how the battle is unfolding. We talk in his conference room in one of several dozen trailers. He’s dressed in the traditional garb of the peshmerga: baggy pants, a thin turban and an embroidered sash around his waist. As he explains the campaign, he points to the maps that line the wall.

The Kurds were rocked by the extremist push toward their capital of Irbil last August, he says. But they regrouped. As the peshmerga advanced, its commanders were able to call in air support from the U.S.-led coalition. They pushed the Islamic State back from Irbil and Makhmur, from the Mosul Dam, from Rabia on the Syrian border, and most recently from the area I visited in Ninevah province in northwestern Iraq.

But success is bringing a dilemma. Who will finish the fight in the north by recapturing Mosul? The Kurds don’t want the job; they have regained most of the territory they lost and know their entry into the Sunni Arab city of Mosul would cause political problems. The Iraqi military and a Sunni tribal militia are getting U.S. training, but they aren’t ready for such a big fight. President Obama has ruled out U.S. ground troops.

Who will retake Mosul? Probably nobody, for a while. Barzani explains the trade-off: “If you want this war to continue for years, take your time and build up the Iraqi army until they’re strong enough to defeat ISIS. But you will leave ISIS free to keep recruiting, organizing and killing. ISIS won’t stand still while you are building capacity.”

Barzani explains why the Islamic State is a formidable adversary: Its best weapons are car bombs; it sent 14 of them against Kurdish lines one day last month. The hardened fighters, many from such places as Chechnya, Kazakhstan and Uzbekistan, blow themselves up rather than surrender. Suicide bombers who think they’re about to meet virgins in heaven are dubbed “grooms.”

But the jihadists have internal problems, too. The foreign fighters, who are called “muhajiroun,” the Arabic word for emigrants, get the pick of captured women and money. The local fighters, known as the “ansar,” are resentful. The jihadists are so nervous about traitors that anyone leaving Mosul is asked to designate a hostage who will be killed if he doesn’t come back. Panicky Islamic State fighters fleeing a battle were told they would be shot if they reached an Islamic State base in Tal Afar.

The United States is counting on the Kurds to hold their ground against these killers while other Iraqi forces get trained. And that brings Barzani to his most important point: The Kurds need U.S. weapons, fast. In particular, they need armored personnel carriers and Humvees to protect their troops, tanks to repel enemy advances, night-vision goggles to detect sneak attacks and small attack helicopters to defend a front that stretches 600 miles.

Barzani’s request seems reasonable, given the crucial role the peshmerga have played in this fight. The trick is to provide weapons to the Kurdish regional government in a way that doesn’t worsen Iraq’s sectarian divisions. Barzani says he would be happy to receive the weapons through the Iraqi government — so long as they’re actually delivered. That strikes me as the right solution, and it should be a priority for the Obama administration.