MOUNT QARACHOGH, Iraq — The black-clad figures are barely visible through binoculars from atop this mountaintop lookout in northern Iraq.

One crouches near stagnant water at the end of a dry riverbed. His companion stands over him and then walks out of view beneath an escarpment, moving without any apparent fear of exposure.

From their position on top of the mountain, the Kurdish peshmerga, the renowned armed forces of the autonomous Kurdistan Regional Government, say Islamic State fighters are living in caves in the no man’s land between Kurdish and Iraqi security forces on the plains below.

This area of northern Iraq includes disputed territories of the central government in Baghdad and the regional authorities in Irbil. It is in ungoverned spaces like this where Kurdish officials say ISIS is rebuilding its networks and running guns between clusters of caves to desert holdouts.

The development is troubling after the grinding struggle and sacrifice involved in rolling back the Islamic State group and its self-proclaimed “caliphate” in Iraq and Syria over the past three years.

President Trump has said the caliphate, which once covered a broad swath of territory and such major cities as Mosul and Fallujah, has been “decimated,” but security analysts say the Islamic State has been scattered but not defeated and still claims the allegiance of thousands of fighters.

U.S. forces are advising and assisting the Iraqi security forces and Kurdish peshmerga to help root out the ISIS remnants. On Sept. 10, U.S. Air Force F-15s and F-35s dropped 80,000 pounds of bombs on an island that the allied coalition said was “infested” with ISIS.

“We’re setting the conditions for our partner forces to continue bringing stability to the region,” Air Force Maj. Gen. Eric Hill, commander of special operations for the Iraqi allied campaign, told reporters at the time. The goal, the general said, was to “disrupt [the Islamic State‘s] ability to hide in the thick vegetation.”

The Pentagon is clearly concerned about a resurgence of the Islamic State, given Iraq’s deeply unsettled political scene. Internal feuding among the Kurds and tensions between Irbil and Baghdad are complicating the mission, according to an inspector general’s second-quarter 2019 report on the state of the Iraqi mission against the Islamic State.

“Deep-seated internal Kurdish political divisions and the Kurds’ continuing dispute with Iraq’s central government over a swath of disputed territory in northern Iraq rich in resources have allowed ISIS insurgents to exploit gaps between [Iraqi security forces] and peshmerga forces, which allows [the Islamic State] to regroup and plan attacks in the region,” according to the inspector general’s review.

The ISIS-controlled island was only 18 miles away from the Kurdish positions, a sign that the fight against the terrorist group is very much alive two years after Mosul was recaptured from ISIS. According to the local Kurdish commanders, Islamic State fighters are infiltrating Sunni Arab villages in the region and exploiting anger among local residents at the presence of Iranian-backed Shiite paramilitaries called Popular Mobilization Forces.

These forces were raised in 2014 by a fatwa from Iraqi Shiite leader Ayatollah Ali al-Sistani, and they became officially part of the Iraqi security forces in March 2018. But efforts to integrate them into the national armed forces away from their sectarian origins have faced hurdles, and there are fears that their heavy-handed tactics and checkpoints will alienate Sunni areas and produce more ISIS recruits.

Essential struggle

For the Kurdistan region, the importance of keeping ISIS defeated is essential. The region lost thousands fighting the extremists from 2014 to 2017 and has since struggled to keep itself free from terrorism.

But that also requires closer coordination between the largely autonomous Kurdish region and the national government in Baghdad, as well as with U.S. and coalition forces stationed in the country. In conversations with two KRG government ministers, a senior adviser and peshmerga generals and commanders, the multifaceted challenges of confronting ISIS today quickly become evident.

The peshmerga require more financial support from Baghdad for salaries, their commanders and officials say. They also need to continue reforms of integrating units, standardizing uniforms and creating an effective supply chain for small arms and other munitions. The Iraqi Constitution is supposed to guarantee this support, but long-standing tensions between Baghdad and Irbil make every part of training and arming the peshmerga a complex process.

Falah Mustafa, senior foreign policy adviser to KRG President Nechirvan Barzani, said in an interview that although the ISIS caliphate has been eliminated, the lure of the Islamic State’s ideology still exists.

“There are groups reorganizing, and we need to work together with Baghdad and the U.S. and the coalition so ISIS will not reemerge,” he said.

Mr. Mustafa said the challenge is not just military, but political and cultural as well. It means engaging with local communities so they see a future for themselves and are not alienated. The Kurdistan region is an island of security and prosperity, he said, and international support is essential in this difficult environment with terrorist threats. Mr. Barzani has said the region is committed to “protect and promote peace in our region and elsewhere.”

Getting to the front lines with the Islamic State these days requires a drive of about one hour outside of Irbil to the desert and mountainous region overlooking the plains that frame the Tigris River. It is among communities in Hawija and the Hamreen mountains where ISIS support first arose.

The Kurdish commanders of the area, called Sector 6, control more than 90 miles of the front lines. ISIS generally operates in small groups and rarely assembles more than 150 men in a cell. But their control allows them to demand taxes from farmers and threaten those who don’t pay.

For now, the anti-Islamic State coalition works closely with the Iraqi army and the peshmerga, but the division on the ground means challenges remain in coordinating the two forces and the territory that separates them. While the Kurdish peshmerga stand guard on their mountains, the Iraqi forces in the plains and desert below are monitoring ISIS.

An Iraqi army operation dubbed Will of Victory has entered its fifth phase. Through binoculars aimed at the ISIS figures coming out for water from their hideouts in caves, it is clear that these operations have a long way to go before victory can be declared.

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