Halabjayi's words sum up the sentiments among the peshmerga and Kurdish officials these days: The blood they are shedding should not go in vain.

“These territories are Kurdistan's now. We will not give them back to the Iraqi army or anybody else,” said the general. “We have had four of our peshmergas die here and several injured for this territory. [IS] exploded eight suicide bombers in this area,” he said.

A few minutes later, he got up with the help of a wooden stick and surveyed the hot, dusty plains of eastern Ninevah province. Occasionally, he shouted an order at the people around him.

“It's a big territory we have taken and we are quite close to Mosul now from this side as well,” Halabjayi told Al-Monitor, as he pointed toward a nearby village.

Gen. Hadi Halabjayi and his peshmerga troops were getting settled in the new territory in the Khazir area they had captured from the Islamic State (IS) in late May after a day and a half of fighting. Sitting under a cloth shade hung between two vehicles, Halabjayi held a piece of shrapnel from a mortar that had landed just minutes before.

In a two-day operation over May 29-30, 5,500 Kurdish peshmerga forces wrested control of nine villages from IS encompassing an area of around 120 square kilometers (46 square miles).

Kurdish authorities described the offensive as "one of the many shaping operations” to increase pressure on IS militants in nearby Mosul leading up to an eventual charge on the major IS stronghold.

But the Kurds have long considered the areas they seized in the recent offensive as part of their homeland. The areas to the immediate east and north of Mosul are among the few remaining patches of territory that Kurds are keen to include in their autonomous zone and make part of a possible future Kurdistan state.

Minority communities such as the Kakais and Shabak resided in the nine villages before IS swept into the Khazir area, some 30 kilometers (19 miles) from Mosul, in August 2014.

Kakais are ethnic Kurds who follow a syncretistic, mystical religion that is believed to have emerged in the Kurdish areas of western Iran in the 14th century.

The Shabak, an ethnic-religious group, are more divided, with some portions of the community seeing themselves as closer to the Kurds and others more pro-Iraqi.

The territory around Khazir, along with a long stretch of the borderland between Kurdish and Arab Iraq spanning Ninevah, Kirkuk, Diyala and Salahuddin provinces, have long been coveted by Kurds as part of their homeland. Successive Iraqi governments have opposed the idea and made efforts to “Arabize” much of these areas, especially under Saddam Hussein. Although the post-Saddam constitution approved in 2005 recognized the ethnic-cleansing efforts against Kurds and other minorities and called for a reversal, those measures were mostly not implemented.

The war with IS has now provided an opportunity for the Kurds to establish control over those areas and fortify their presence there. In the absence of a strong rival military force, the Kurds appear to be in control of the areas known as the “disputed territories” in Article 140 of Iraq's constitution.

The area around Mosul is of particular interest to the Kurds, as it provides strategic depth that can also act as a security buffer zone between Iraqi Kurdistan's capital, Erbil, and the city of Mosul, which has been volatile for most of the past decade. The situation is unlikely to change anytime soon, given that many expect rivalries there to continue in the post-IS phase.

“The Kurds do not want the Iraqi central government, particularly Shia paramilitary groups under the umbrella of the [Popular Mobilization Units], to exploit the recapture of Mosul to re-impose Baghdad’s authority in the area,” wrote Renad Mansour, a fellow with Carnegie Middle East Center, in a May 20 report about the Kurdish strategy in Mosul in the post-IS period.

The return of the Iraqi military forces, and even possibly their Shiite paramilitary allies, to Ninevah province to fight IS will eventually pose a major challenge to the Kurds' domination in the parts of Ninevah that they control.

The peshmerga forces were quick to fortify their positions here, as multiple bulldozers dug dirt berms along the approximately 20-kilometer (12-mile) stretch of land spanning the eastern Mosul countryside.

At the southernmost tip of the new territory in Wardak village, Capt. Nasraddin Karim and his men inspected a house where IS had made bombs. The products were neatly collected in a corner of what appeared to be the living room. Karim pointed out writing on the wall that read, “The Islamic State will stay by God's will” and told his fellow fighters, “They fled.” The IS militants seemed to have abandoned the place hastily, as some bomb-making material, a pink paste, was left on a small plate.

IS might be gone from this area, but conflict is unlikely to depart this place for years to come.